Advertisements
Advertisements
Question
Construct the truth table of the following statement pattern.
∼ p ∧ [(p ∨ ∼ q) ∧ q]
Solution
p | q | ∼ p | ∼ q | p ∨ ∼ q | (p ∨ ∼ q) ∧ q | ∼ p ∧ [(p ∨ ∼ q) ∧ q] |
T | T | F | F | T | T | F |
T | F | F | T | T | F | F |
F | T | T | F | F | F | F |
F | F | T | T | T | F | F |
APPEARS IN
RELATED QUESTIONS
Using truth table prove that p ↔ q = (p ∧ q) ∨ (~p ∧ ~q).
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
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.
Nagpur is in Maharashtra and Chennai is in Tamil Nadu.
Write the following compound statement symbolically.
Angle is neither acute nor obtuse.
Write the following compound statement symbolically.
If Δ ABC is right-angled at B, then m∠A + m∠C = 90°
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 ∨ r)
Construct the truth table of the following statement pattern.
(∼ p → ∼ q) ∧ (∼ q → ∼ p)
Construct the truth table of the following statement pattern.
(q → p) ∨ (∼ p ↔ q)
If p ∧ q is false and p ∨ q is true, then ______ is not true.
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)]
Construct the truth table of the following:
[(∼p ∨ q) ∧ (q → r)] → (p → r)
Determine the truth values of p and q in the following case:
(p ∨ q) is T and (p ∧ q) is T
Express the following statement in symbolic form.
e is a vowel or 2 + 3 = 5
Express the following statement in symbolic form.
Milk is white or grass is green.
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 following statement.
The Himalayas are the highest mountains but they are part of India in the North East.
Write the negation of the following statement.
− 3 is a natural number.
Write the negation of the following statement.
2 + 3 ≠ 5
Write the truth value of the negation of the following statement.
`sqrt5` is an irrational number.
Write the following statement in symbolic form.
If triangle is equilateral then it is equiangular.
Write the following statement in symbolic form.
Even though it is not cloudy, it is still raining.
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.
If a joint venture is a temporary partnership, then discount on purchase is credited to the supplier.
Find the truth value of the following statement.
Neither 27 is a prime number nor divisible by 4.
If p and q are true and r and s are false, find the truth value of the following compound statement.
(p → q) ↔ ~(p ∨ q)
If p and q are true and r and s are false, find the truth value of the following compound statement.
[(p ∨ s) → r] ∨ ~ [~ (p → q) ∨ s]
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 a holiday and Ram studies on holiday.
If p : He swims
q : Water is warm
Give the verbal statement for the following symbolic statement.
q → p
Fill in the blanks :
Negation of “some men are animal” is –––––––––.
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.
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.
It is not true that intelligent persons are neither polite nor helpful.
If p : Proof is lengthy.
q : It is interesting.
Express the following statement in symbolic form.
If proof is lengthy then it is interesting.
If p : Proof is lengthy.
q : It is interesting.
Express the following statement in symbolic form.
It is not true that the proof is lengthy but it is interesting.
If p : Proof is lengthy.
q : It is interesting.
Express the following statement in symbolic form.
It is interesting iff the proof is lengthy.
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
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 → r
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
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.
If x ∈ A ∩ B, then x ∈ A and x ∈ B.
Rewrite the following statement without using the connective ‘If ... then’.
If 10 − 3 = 7 then 10 × 3 ≠ 30.
Rewrite the following statement without using the connective ‘If ... then’.
If it rains then the principal declares a holiday.
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.
Write the negation of the following statement.
7 is prime number and Tajmahal is in Agra.
Write the negation of the following statement.
10 > 5 and 3 < 8
Write the negation of the following statement.
I will have tea or coffee.
Write the negation of the following statement.
∀ n ∈ N, n + 3 > 9.
Write the negation of the following statement.
∃ x ∈ A, such that x + 5 < 11.
Negation of p → (p ˅ ∼ q) is ______
A biconditional statement is the conjunction of two ______ statements.
If p → q is an implication, then the implication ∼ q → ∼ p is called its
The negation of the statement (p ˄ q) `→` (r ˅ ∼ p) is ______.
Find the negation of 10 + 20 = 30
Write the following compound statements symbolically.
Triangle is equilateral or isosceles
Write the following statements in symbolic form
Even though it is not cloudy, it is still raining
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:
A biconditional statement is the conjunction of two ______ statements
State whether the following statement is True or False:
The converse of inverse of ~ p → q is q → ~ p
Write the following statements in symbolic form.
If Qutub – Minar is in Delhi then Taj-Mahal is in Agra
Given 'p' and 'q' as true and 'r' as false, the truth values of p v (q ∧ ~r) and (p → r) ∧ q are respectively
If q: There are clouds in the sky then p: it is raining. The symbolic form is ______
If p and q are true and rands are false statements, then which of the following is true?
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 ______
The negation of ∼s ∨ (∼r ∧ s) 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 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 ______.
Write the following statement in symbolic form.
It is not true that `sqrt(2)` is a rational number.
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
From the following set of statements, select two statements which have similar meaning.
- If a man is judge, then he is honest.
- If a man is not a judge, then he is not honest.
- If a man is honest, then he is a judge.
- If a man is not honest, then he is not a judge.
If p, q are true statements and r, s are false statements, then write the truth value of the compound statement
(p `→` ∼ r) `→` (q ∧ s)
Using the statements
p: Seema is fat,
q: Seema is happy,
Write the following statements in symbolic form;
- Seema is thin and happy.
- If Seema is fat then she is unhappy.
Write the negation of (p `leftrightarrow` q).
Using truth table prove that:
~ (p `leftrightarrow` q) ≡ (p ∧ ~ q) ∨ (q ∧ ~ p)
Construct the truth table for the statement pattern:
[(p → q) ∧ q] → p