Advertisements
Advertisements
प्रश्न
Find the truth value of the following statement.
It is not true that 3 − 7i is a real number.
Advertisements
उत्तर
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
संबंधित प्रश्न
Examine whether each of the following statement patterns is a tautology or a contradiction or a contingency.
[~(~p ∧ ~q)] v q
Using truth table prove that ∼p ˄ q ≡ (p ˅ q) ˄ ∼p
Write the following compound statement symbolically.
If ΔABC is right-angled at B, then m∠A + m∠C = 90°.
Construct the truth table of the following statement pattern.
p → [∼ (q ∧ r)]
Construct the truth table of the following statement pattern.
[p → (q → r)] ↔ [(p ∧ q) → r]
Construct the truth table of the following statement pattern.
(p ∨ ∼ q) → (r ∧ p)
Construct the truth table of the following:
p → (q → p)
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.
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.
Kavita is brilliant and brave.
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.
Assuming the first statement p and second as q. Write the following statement in symbolic form.
Even though it is not cloudy, it is still raining.
Rewrite the following statement without using the connective ‘If ... then’.
If it rains then the principal declares a holiday.
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.
If p → q is an implication, then the implication ∼ q → ∼ p is called its
Write the following statements in symbolic form
Even though it is not cloudy, it is still raining
Choose the correct alternative:
A biconditional statement is the conjunction of two ______ statements
State whether the following statement is True or False:
The converse of inverse of ~ p → q is q → ~ p
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 ______.
Write the contrapositive of the inverse of the statement:
‘If two numbers are not equal, then their squares are not equal’.
Using truth table prove that:
~ (p `leftrightarrow` q) ≡ (p ∧ ~ q) ∨ (q ∧ ~ p)
