Advertisements
Advertisements
Question
Find the truth value of the following statement.
It is not true that 3 − 7i is a real number.
Advertisements
Solution
Let p : 3 – 7i is a real number.
The truth value of p is F.
The given statement in symbolic form is ~p.
∴ ~ p ≡ ~ F ≡ T
∴ Truth value of the given statement is T.
APPEARS IN
RELATED QUESTIONS
Using truth table prove that ∼p ˄ q ≡ (p ˅ q) ˄ ∼p
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:
(∼p ∨ ∼q) ↔ [∼(p ∧ q)]
Construct the truth table of the following:
[(∼p ∨ q) ∧ (q → r)] → (p → r)
Express the following statement in symbolic form.
Mango is a fruit but potato is a vegetable.
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 negation of the following statement.
− 3 is a natural number.
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.
If p : He swims
q : Water is warm
Give the verbal statement for the following symbolic statement.
q ∧ ~ p
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.
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
Rewrite the following statement without using the connective ‘If ... then’.
If it rains then the principal declares a holiday.
Write the negation of the following statement.
∃ x ∈ A, such that x + 5 < 11.
If p → q is an implication, then the implication ∼ q → ∼ p is called its
Write the following compound statements symbolically.
Triangle is equilateral or isosceles
Write the following statement in symbolic form:
Milk is white if and only if the sky is not blue.
Using truth table prove that p ˅ (q ˄ r) ≡ (p ˅ q) ˄ (p ˅ r)
If q: There are clouds in the sky then p: it is raining. The symbolic form is ______
Let p : 7 is not greater than 4 and q : Paris is in France by two statements. Then ∼(p ∨ q) is the statement ______
The inverse of the statement "If its quality is good. then it is expensive.", is ______
The negation of the statement: "Getting above 95% marks is a necessary condition for Hema to get admission in good college'' is ______
Write the following statement in symbolic form.
It is not true that `sqrt(2)` is a rational number.
Construct the truth table for the statement pattern:
[(p → q) ∧ q] → p
