Advertisements
Advertisements
Question
Without using truth table prove that:
~ (p ∨ q) ∨ (~ p ∧ q) ≡ ~ p
Advertisements
Solution
We have,
L.H.S. = ∼(p ∨ q) ∨ (∼p ∧ q)
= (∼ p ∧ ∼q) ∨ (∼p ∧ q) ....(By De Morgan's Law)
= ∼p ∧ (∼q ∨ q) ....(By Distributive Law)
= ∼p ∧ T ....(By Complement Law)
= ∼p
R.H.S. = ∼p
L.H.S. = R.H.S.
RELATED QUESTIONS
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 the following logical equivalence:
(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)
Determine the truth values of p and q in the following case:
(p ∨ q) is T and (p ∨ q) → q is F
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.
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 truth value of the negation of the following statement.
London is in England.
Write the following statement in symbolic form.
If Kutub-Minar is in Delhi then Taj-Mahal is in Agra.
Find the truth value of the following statement.
It is not true that 3 − 7i is a real number.
Find the truth value of the following statement.
If a joint venture is a temporary partnership, then discount on purchase is credited to the supplier.
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.
If Sunday is not holiday then Ram studies on holiday.
Fill in the blanks :
Conjunction of two statement p and q is symbolically written as ______.
Negation of “some men are animal” is ______.
State whether the following statement is True or False:
The negation of 10 + 20 = 30 is, it is false that 10 + 20 ≠ 30.
Assuming the first statement p and second as q. Write the following statement in symbolic form.
3 is prime number if 3 is perfect square number.
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 conditional –
(Hint : p → q ≡ ∼ p ∨ q)
If demand falls, then price does not increase.
Assuming the following statement.
p : Stock prices are high.
q : Stocks are rising.
to be true, find the truth value of the following.
Stock prices are high or stocks are not rising iff stocks are rising.
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.
7 is prime number and Tajmahal is in Agra.
Write the negation of the following statement.
I will have tea or coffee.
Find the negation of 10 + 20 = 30
Write the following compound statements symbolically.
Triangle is equilateral or isosceles
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°”
If p, q are true statement and r is false statement, then which of the following statements is a true statement.
The symbolic form of the following circuit is (where p, q represents switches S1 and S2 closed respectively)
Which of the following is false?
If p and q are true and rands are false statements, then which of the following is true?
Which of the following is NOT true for p → q.
The inverse of the statement "If its quality is good. then it is expensive.", is ______
Write the converse, inverse, and contrapositive of the statement. "If 2 + 5 = 10, then 4 + 10 = 20."
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?
Converse of the statement q `rightarrow` p is ______.
Write the following statement in symbolic form.
4 is an odd number if 3 is not a prime factor of 6.
Write the negation of p ↔ q.
Construct the truth table for the statement pattern:
[(p → q) ∧ q] → p
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?
