Advertisements
Advertisements
Question
Find the truth value of the following statement.
Neither 27 is a prime number nor divisible by 4.
Advertisements
Solution
Let p : 27 is a prime number.
q : 27 is divisible by 4.
The truth values of p and q are F and F respectively.
The given statement in symbolic form is ~ p ∧ ~ q.
∴ ~ p ∧ ~ q ≡ ~ F ∧ ~ F ≡ T ∧ T ≡ T
∴ Truth value of the given statement is T.
APPEARS IN
RELATED QUESTIONS
Using truth table, prove the following logical equivalence:
(p ∧ q) → r ≡ p → (q → r)
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:
(∼p ∨ ∼q) ↔ [∼(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.
I like playing but not singing.
Write the truth value of the following statement.
A quadratic equation has two distinct roots or 6 has three prime factors.
If p : He swims
q : Water is warm
Give the verbal statement for the following symbolic statement.
~ (p ∨ q)
Assuming the first statement p and second as q. Write the following statement in symbolic form.
Kavita is brilliant and brave.
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) ∨ 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)
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
Write the negation of the following.
If ∆ABC is not equilateral, then it is not equiangular.
Rewrite the following statement without using the connective ‘If ... then’.
If 10 − 3 = 7 then 10 × 3 ≠ 30.
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.
The negation of the statement (p ˄ q) `→` (r ˅ ∼ p) is ______.
Write the negation of the statement “An angle is a right angle if and only if it is of measure 90°”
Choose the correct alternative:
Negation of p → (p ˅ ~q) is
Write the negation of the statement “An angle is a right angle if and only if it is of measure 90°”
If p : Every natural number is a real number.
q : Every integer is a complex number. Then truth values of p → q and p ↔ q are ______ and ______ respectively.
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 ______
Which of the following is logically equivalent to `∼(∼p \implies q)`?
Converse of the statement q `rightarrow` p is ______.
If a statement b has truth value False and \[(p\wedge q)\leftrightarrow r\] has truth value True, then which of the following has truth value True?
