Advertisements
Advertisements
Question
Find the truth value of the following statement.
3 is a prime number and an odd number.
Advertisements
Solution
Let p : 3 is a prime number.
q : 3 is an odd number.
The truth values of p and q are T and T respectively.
The given statement in symbolic form is p ∧ q.
∴ p ∧ q ≡ T ∧ T ≡ T
∴ Truth value of the given statement is T.
APPEARS IN
RELATED QUESTIONS
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 ∧ r)]
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:
[(∼p ∨ q) ∧ (q → r)] → (p → r)
Express the following statement in symbolic form.
e is a vowel or 2 + 3 = 5
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.
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:
p ↔ ~ q
Fill in the blanks :
Conjunction of two statement p and q is symbolically written as ______.
Assuming the first statement p and second as q. Write the following statement in symbolic form.
3 is prime number if 3 is perfect square number.
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.
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.
Write the negation of the following.
If ∆ABC is not equilateral, then it is not equiangular.
Write the negation of the following statement.
7 is prime number and Tajmahal is in Agra.
Find the negation of 10 + 20 = 30
Write the following compound statements symbolically.
Triangle is equilateral or isosceles
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 statement in symbolic form:
Milk is white if and only if the sky is not blue.
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 c denotes the contradiction then the dual of the compound statement ∼p ∧ (q ∨ c) is ______
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?
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.
Write the negation of p ↔ q.
