Advertisements
Advertisements
प्रश्न
Construct the truth table of the following:
∼ (∼p ∧ ∼q) ∨ q
Advertisements
उत्तर
| p | q | ∼p | ∼q | ∼p ∧ ∼q | ∼ (∼P ∧ ∼q) | ∼ (∼p ∧ ∼q) ∨ q |
| T | T | F | F | F | T | T |
| T | F | F | T | F | T | T |
| F | T | T | F | F | T | T |
| F | F | T | T | T | F | F |
[Note: Answer in the textbook is incorrect.]
APPEARS IN
संबंधित प्रश्न
Using truth table, prove the following logical equivalence:
(p ∧ q) → r ≡ p → (q → r)
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 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) ↔ (q ∨ r)
Construct the truth table of the following statement pattern.
∼ p ∧ [(p ∨ ∼ q) ∧ q]
Construct the truth table of the following statement pattern.
(∼ p → ∼ q) ∧ (∼ 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.
Mango is a fruit but potato is a vegetable.
Express the following statement in symbolic form.
Even though it is cloudy, it is still raining.
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 truth value of the negation of the following statement.
`sqrt5` is an irrational number.
Write the following statement in symbolic form.
If triangle is equilateral then it is equiangular.
If p and q are true and r and s are false, find the truth value of the following compound statement.
~ [p ∨ (r ∧ s)] ∧ ~ [(r ∧ ~ s) ∧ q]
Assuming that the following statement is true,
p : Sunday is holiday,
q : Ram does not study on holiday,
find the truth values of the following statements.
Sunday is not holiday or Ram studies on holiday.
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.
It is not true that intelligent persons are neither polite nor helpful.
Assuming the first statement p and second as q. Write the following statement in symbolic form.
If the question paper is not easy then we shall not pass.
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.
It is interesting iff the proof is lengthy.
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.
Kanchanganga is in India and Everest is in Nepal.
Write the negation of the following.
If x ∈ A ∩ B, then x ∈ A and x ∈ B.
Write the negation of the following statement.
10 > 5 and 3 < 8
A biconditional statement is the conjunction of two ______ statements.
The negation of the statement (p ˄ q) `→` (r ˅ ∼ p) is ______.
Find the negation of 10 + 20 = 30
Write the negation of the statement “An angle is a right angle if and only if it is of measure 90°”
Write the following statements in symbolic form
Even though it is not cloudy, it is still raining
Using truth table prove that p ˅ (q ˄ r) ≡ (p ˅ q) ˄ (p ˅ r)
Without using truth table show that -
(p ˅ q) ˄ (∼p v ∼q) ≡ (p ∧ ∼q) ˄ (∼p ∧ q)
Negation of “Some men are animal” is ______.
Write the negation of the statement “An angle is a right angle if and only if it is of measure 90°”
Write the following statements in symbolic form.
If Qutub – Minar is in Delhi then Taj-Mahal is in Agra
The Boolean expression ∼(q ⇒ ∼p) is equivalent to: ______
The negation of ∼s ∨ (∼r ∧ s) is equivalent to ______
The Boolean expression ∼(p ∨ q) ∨ (∼p ∧ q) is equivalent to ______
Converse of the statement q `rightarrow` p is ______.
The statement ∼(p ↔ ∼q) is ______.
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
