Advertisements
Advertisements
प्रश्न
Construct the truth table of the following:
(∼p ∨ ∼q) ↔ [∼(p ∧ q)]
Advertisements
उत्तर
| p | q | ∼p | ∼q | ∼p ∨ ∼q | p∧q | ∼ (p∧q) | (∼p ∨ ∼q) ↔ [∼ (p∧q)] |
| T | T | F | F | F | T | F | T |
| T | F | F | T | T | F | T | T |
| F | T | T | F | T | F | T | T |
| F | F | T | T | T | F | T | 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
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
Write the following compound statement symbolically.
If ΔABC is right-angled at B, then m∠A + m∠C = 90°.
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 ∧ [(p ∨ ∼ q) ∧ q]
Construct the truth table of the following statement pattern.
(p ∨ ∼ q) → (r ∧ p)
Construct the truth table of the following:
∼ (∼p ∧ ∼q) ∨ q
Determine the truth values of p and q in the following case:
(p ∨ q) is T and (p ∧ q) is T
Determine the truth values of p and q in the following case:
(p ∨ q) is T and (p ∨ q) → q is F
Express the following statement in symbolic form.
I like playing but not singing.
Express the following statement in symbolic form.
Even though it is cloudy, it is still raining.
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.
16 is an even number and 8 is a perfect square.
Write the negation of the following statement.
− 3 is a natural number.
Write the following statement in symbolic form.
It is not true that “i” is a real number.
If p and q are true and r and s are false, find the truth value of the following compound statement.
(p → q) ∨ (r ∧ s)
If p and q are true and r and s are false, find the truth value of the following compound statement.
~ [(~ p ∨ s) ∧ (~ q ∧ r)]
If p and q are true and r and s are false, find the truth value of the following compound statement.
(p → q) ↔ ~(p ∨ q)
If p : He swims
q : Water is warm
Give the verbal statement for the following symbolic statement.
q → p
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.
The Sun has set and Moon has risen.
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.
The necessary condition for existence of a tangent to the curve of the function is continuity.
Assuming the first statement p and second as q. Write the following statement in symbolic form.
x3 + y3 = (x + y)3 if xy = 0.
If p : Proof is lengthy.
q : It is interesting.
Express the following statement in symbolic form.
Proof is lengthy and it is not interesting.
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 → 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
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.
Write the negation of the following.
Ramesh is intelligent and he is hard working.
Write the negation of the following.
If x ∈ A ∩ B, then x ∈ A and x ∈ B.
If p → q is an implication, then the implication ∼ q → ∼ p is called its
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 Kutab – Minar is in Delhi then Taj - Mahal is in Agra
Write the following statements in symbolic form
Even though it is not cloudy, it is still raining
Without using truth table show that -
(p ˅ q) ˄ (∼p v ∼q) ≡ (p ∧ ∼q) ˄ (∼p ∧ q)
Choose the correct alternative:
Negation of p → (p ˅ ~q) is
Given 'p' and 'q' as true and 'r' as false, the truth values of p v (q ∧ ~r) and (p → r) ∧ q are respectively
The symbolic form of the following circuit is (where p, q represents switches S1 and S2 closed respectively)

The negation of ∼s ∨ (∼r ∧ s) is equivalent to ______
The logical statement (∼p → q) ∧ (q → p) is equivalent to: ______
Express the following compound statement symbolically:
3 + 8 ≥ 12 if and only if 5 × 4 ≤ 25
Let p: I am brave.
q: I will climb the Mount Everest.
The symbolic form of a statement,
‘I am neither brave nor I will climb the mount Everest’ is
