Advertisements
Advertisements
प्रश्न
Find the truth value of the following statement.
Neither 27 is a prime number nor divisible by 4.
Advertisements
उत्तर
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
संबंधित प्रश्न
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.
The angle is right angle if and only if it is of measure 90°.
Write the following compound statement symbolically.
Angle is neither acute nor obtuse.
Construct the truth table of the following statement pattern.
∼ p ∧ [(p ∨ ∼ q) ∧ q]
Construct the truth table of the following:
p → (q → p)
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.
Even though it is cloudy, it is still raining.
Write the negation of the following statement.
− 3 is a natural number.
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.
The drug is effective though it has side effects.
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.
If p : Proof is lengthy.
q : It is interesting.
Express the following statement in symbolic form.
If proof is lengthy then 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 ∨ r)
Rewrite the following statement without using conditional –
(Hint : p → q ≡ ∼ p ∨ q)
If demand falls, then price does not increase.
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
The negation of the statement (p ˄ q) `→` (r ˅ ∼ p) is ______.
Without using truth table prove that:
~ (p ∨ q) ∨ (~ p ∧ q) ≡ ~ p
Which of the following is NOT true for p → q.
The Boolean expression ∼(q ⇒ ∼p) is equivalent to: ______
The Boolean expression ∼(p ∨ q) ∨ (∼p ∧ q) is equivalent to ______
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 negation of the statement: "Getting above 95% marks is a necessary condition for Hema to get admission in good college'' is ______
Conditional of p → q is equivalent to p → ∼ q.
Let p, q and r be any three logical statements. Which of the following is true?
