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प्रश्न
If p → q is an implication, then the implication ∼ q → ∼ p is called its
पर्याय
Converse
Contrapositive
Inverse
Alternative
उत्तर
Contrapositive
संबंधित प्रश्न
Using truth table prove that p ↔ q = (p ∧ q) ∨ (~p ∧ ~q).
Using truth table, prove the following logical equivalence:
(p ∧ q) → r ≡ p → (q → r)
Write down the following statements in symbolic form :
(A) A triangle is equilateral if and only if it is equiangular.
(B) Price increases and demand falls
Using truth table prove that ∼p ˄ q ≡ (p ˅ q) ˄ ∼p
Using the truth table, prove the following logical equivalence :
p ↔ q ≡ (p ∧ q) ∨ (~p ∧ ~q)
Evaluate: ∫ x . log x dx
Write converse, inverse contrapositive of the statement "If two triangles are not congruent then their areas are not equal.
Write the following compound statement symbolically.
Angle is neither acute nor obtuse.
Write the following compound statement symbolically.
Hima Das wins gold medal if and only if she runs fast.
Write the following compound statement symbolically.
x is not irrational number but is a square of an integer.
Construct the truth table of the following statement pattern.
[(p → q) ∧ q] → p
Construct the truth table of the following statement pattern.
(p ∧ ∼q) ↔ (p → q)
Construct the truth table of the following statement pattern.
(p ∧ q) ↔ (q ∨ r)
Construct the truth table of the following statement pattern.
p → [∼ (q ∧ r)]
Construct the truth table of the following statement pattern.
∼ p ∧ [(p ∨ ∼ q) ∧ q]
Construct the truth table of the following statement pattern.
(q → p) ∨ (∼ p ↔ q)
Construct the truth table of the following statement pattern.
[p → (q → r)] ↔ [(p ∧ q) → r]
Construct the truth table of the following statement pattern.
(p ∨ ∼ q) → (r ∧ p)
Construct the truth table of the following:
p → (q → p)
Construct the truth table of the following:
(∼p ∨ ∼q) ↔ [∼(p ∧ q)]
Construct the truth table of the following:
[(p ∧ q) ∨ r] ∧ [∼r ∨ (p ∧ q)]
Determine the truth values of p and q in the following case:
(p ∧ q) is F and (p ∧ q) → q is T
Express the following statement in symbolic form.
Milk is white or grass is green.
Express the following statement in symbolic form.
I like playing but not singing.
Express the following statement in symbolic form.
Even though it is cloudy, it is still raining.
Write the truth value of the following statement.
Earth is a planet and Moon is a star.
Write the truth value of the following statement.
A quadratic equation has two distinct roots or 6 has three prime factors.
Write the truth value of the negation of the following statement.
`sqrt5` is an irrational number.
Write the truth value of the negation of the following statement.
London is in England.
Write the truth value of the negation of the following statement.
For every x ∈ N, x + 3 < 8.
Write the following statement in symbolic form.
If triangle is equilateral then it is equiangular.
Write the following statement in symbolic form.
It is not true that “i” is a real number.
Write the following statement in symbolic form.
Even though it is not cloudy, it is still raining.
Write the following statement in symbolic form.
If Kutub-Minar is in Delhi then Taj-Mahal is in Agra.
Find the truth value of the following statement.
It is not true that 3 − 7i is a real number.
Find the truth value of the following statement.
Every accountant is free to apply his own accounting rules if and only if machinery is an asset.
If p and q are true and r and s are false, find the truth value of the following compound statement.
p ∧ (q ∧ r)
If p and q are true and r and s are false, find the truth value of the following compound statement.
~ [(~ p ∨ s) ∧ (~ q ∧ r)]
If p and q are true and r and s are false, find the truth value of the following compound statement.
~ [p ∨ (r ∧ s)] ∧ ~ [(r ∧ ~ s) ∧ q]
Assuming that the following statement is true,
p : Sunday is holiday,
q : Ram does not study on holiday,
find the truth values of the following statements.
Sunday is not holiday or Ram studies on holiday.
Assuming that the following statement is true,
p : Sunday is holiday,
q : Ram does not study on holiday,
find the truth values of the following statements.
If Sunday is not holiday then Ram studies on holiday.
If p : He swims
q : Water is warm
Give the verbal statement for the following symbolic statement.
p ↔ ~ q
State whether the following statement is True or False:
The negation of 10 + 20 = 30 is, it is false that 10 + 20 ≠ 30.
Assuming the first statement p and second as q. Write the following statement in symbolic form.
The Sun has set and Moon has risen.
Assuming the first statement p and second as q. Write the following statement in symbolic form.
If Kiran drives the car, then Sameer will walk.
Assuming the first statement p and second as q. Write the following statement in symbolic form.
The necessary condition for existence of a tangent to the curve of the function is continuity.
Assuming the first statement p and second as q. Write the following statement in symbolic form.
To be brave is necessary and sufficient condition to climb the Mount Everest.
Assuming the first statement p and second as q. Write the following statement in symbolic form.
x3 + y3 = (x + y)3 if xy = 0.
Assuming the first statement p and second as q. Write the following statement in symbolic form.
The drug is effective though it has side effects.
Assuming the first statement p and second as q. Write the following statement in symbolic form.
If a real number is not rational, then it must be irrational.
Assuming the first statement p and second as q. Write the following statement in symbolic form.
It is not true that Ram is tall and handsome.
Assuming the first statement p and second as q. Write the following statement in symbolic form.
If the question paper is not easy then we shall not pass.
If p : Proof is lengthy.
q : It is interesting.
Express the following statement in symbolic form.
If proof is lengthy then it is interesting.
Let p : Sachin wins the match.
q : Sachin is a member of Rajya Sabha.
r : Sachin is happy.
Write the verbal statement of the following.
∼ p ∨ q
Let p : Sachin wins the match.
q : Sachin is a member of Rajya Sabha.
r : Sachin is happy.
Write the verbal statement of the following.
p → q
Let p : Sachin wins the match.
q : Sachin is a member of Rajya Sabha.
r : Sachin is happy.
Write the verbal statement of the following.
(p ∧ q) ∧ ∼ r
Rewrite the following statement without using conditional –
(Hint : p → q ≡ ∼ p ∨ q)
If price increases, then demand falls.
Write the negation of the following.
If ∆ABC is not equilateral, then it is not equiangular.
Write the negation of the following.
An angle is a right angle if and only if it is of measure 90°.
Assuming the following statement.
p : Stock prices are high.
q : Stocks are rising.
to be true, find the truth value of the following.
Stock prices are high or stocks are not rising iff stocks are rising.
Consider the following statements.
- If D is dog, then D is very good.
- If D is very good, then D is dog.
- If D is not very good, then D is not a dog.
- If D is not a dog, then D is not very good.
Identify the pairs of statements having the same meaning. Justify.
A biconditional statement is the conjunction of two ______ statements.
The negation of the statement (p ˄ q) `→` (r ˅ ∼ p) is ______.
Find the negation of 10 + 20 = 30
Without using truth table prove that:
~ (p ∨ q) ∨ (~ p ∧ q) ≡ ~ p
Write the negation of the statement “An angle is a right angle if and only if it is of measure 90°”
Write the following statements in symbolic form
Milk is white if and only if the sky is not blue
Write the following statements in symbolic form
If Kutab – Minar is in Delhi then Taj - Mahal is in Agra
Write the following statements in symbolic form
Even though it is not cloudy, it is still raining
Using truth table prove that p ˅ (q ˄ r) ≡ (p ˅ q) ˄ (p ˅ r)
Without using truth table show that -
(p ˅ q) ˄ (∼p v ∼q) ≡ (p ∧ ∼q) ˄ (∼p ∧ q)
Write the negation of p → q
Choose the correct alternative:
Negation of p → (p ˅ ~q) is
State whether the following statement is True or False:
The converse of inverse of ~ p → q is q → ~ p
Negation of “Some men are animal “ is ______
Write the negation of the statement “An angle is a right angle if and only if it is of measure 90°”
Write the following statements in symbolic form.
If Qutub – Minar is in Delhi then Taj-Mahal is in Agra
If (p ∧ ~ r) → (~ p ∨ q) is a false statement, then respective truth values of p, q and r are ______.
If p, q are true statement and r is false statement, then which of the following statements is a true statement.
The symbolic form of the following circuit is (where p, q represents switches S1 and S2 closed respectively)
If c denotes the contradiction then the dual of the compound statement ∼p ∧ (q ∨ c) is ______
Which of the following is false?
Let p : 7 is not greater than 4 and q : Paris is in France by two statements. Then ∼(p ∨ q) is the statement ______
The negation of (p ∨ ∼q) ∧ q is ______
Which of the following is NOT true for p → q.
The Boolean expression ∼(q ⇒ ∼p) is equivalent to: ______
The statement, 'If I go to school, then I will get knowledge' is equivalent to ______
The Boolean expression ∼(p ∨ q) ∨ (∼p ∧ q) is equivalent to ______
Let S be a non-empty subset of R. Consider the following statement:
p: There is a rational number x ∈ S such that x > 0. Which of the following statements is the negation of the statement p?
The negation of the statement: "Getting above 95% marks is a necessary condition for Hema to get admission in good college'' is ______
The logical statement (∼p → q) ∧ (q → p) is equivalent to: ______
Write the converse, inverse, and contrapositive of the statement. "If 2 + 5 = 10, then 4 + 10 = 20."
Let p, q and r be any three logical statements. Which of the following is true?
Which of the following is logically equivalent to `∼(∼p \implies q)`?
If p : A man is happy, q : A man is rich, then the symbolic form of ‘A man is neither happy nor rich is ______.
Converse of the statement q `rightarrow` p is ______.
Write the following statement in symbolic form.
4 is an odd number if 3 is not a prime factor of 6.
The statement ∼(p ↔ ∼q) is ______.
Express the following compound statement symbolically:
Delhi is in India but Dhaka is not in Sri Lanka
Express the following compound statement symbolically:
3 + 8 ≥ 12 if and only if 5 × 4 ≤ 25
Write the contrapositive of the inverse of the statement:
‘If two numbers are not equal, then their squares are not equal’.
Using truth table prove that:
~ (p `leftrightarrow` q) ≡ (p ∧ ~ q) ∨ (q ∧ ~ p)
