Advertisements
Advertisements
Question
Write the truth value of the following statement.
16 is an even number and 8 is a perfect square.
Solution
Let p : 16 is an even number.
q : 8 is a perfect square.
The truth values of p and q are T and F respectively.
The given statement in symbolic form is p ∧ q.
∴ p ∧ q ≡ T ∧ F ≡ F
∴ Truth value of the given statement is F.
APPEARS IN
RELATED QUESTIONS
Using truth table, prove the following logical equivalence:
(p ∧ q) → r ≡ p → (q → r)
Using the truth table, prove the following logical equivalence :
p ↔ q ≡ (p ∧ q) ∨ (~p ∧ ~q)
Construct the truth table of the following:
∼ (∼p ∧ ∼q) ∨ q
Express the following statement in symbolic form.
e is a vowel or 2 + 3 = 5
Write the truth value of the following statement.
A quadratic equation has two distinct roots or 6 has three prime factors.
Write the negation of the following statement.
It is false that Nagpur is capital of Maharashtra
Write the truth value of the negation of the following statement.
`sqrt5` is an irrational 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.
Milk is white if and only if the sky is not blue.
Write the following statement in symbolic form.
Stock prices are high if and only if stocks are rising.
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.
If a joint venture is a temporary partnership, then discount on purchase is credited to the supplier.
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 → 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 ∨ (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.
If p : He swims
q : Water is warm
Give the verbal statement for the following symbolic statement.
p ↔ ~ q
If p : He swims
q : Water is warm
Give the verbal statement for the following symbolic statement.
~ (p ∨ q)
Fill in the blanks :
Conjunction of two statement p and q is symbolically written as ______.
Fill in the blanks :
Negation of “some men are animal” is –––––––––.
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.
It is not true that Ram is tall and handsome.
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.
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
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.
∀ n ∈ N, n + 3 > 9.
Find the negation of 10 + 20 = 30
State whether the following statement is True or False:
The converse of inverse of ~ p → q is q → ~ p
If p, q are true statement and r is false statement, then which of the following statements is a true statement.
The negation of (p ∨ ∼q) ∧ q is ______
Which of the following is NOT true for p → q.
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 logical statement (∼p → q) ∧ (q → p) is equivalent to: ______
Conditional of p → q is equivalent to p → ∼ q.
Express the following compound statement symbolically:
Delhi is in India but Dhaka is not in Sri Lanka
Write the contrapositive of the inverse of the statement:
‘If two numbers are not equal, then their squares are not equal’.
