Advertisements
Advertisements
Question
Construct the truth table of the following statement pattern.
[(p → q) ∧ q] → p
Advertisements
Solution
Here are two statements and three connectives.
∴ There are 2 × 2 = 4 rows and 2 + 3 = 5 columns in the truth table.
| p | q | p → q | (p → q) ∧ q | [(p → q) ∧ q] → p |
| T | T | T | T | T |
| T | F | F | F | T |
| F | T | T | T | F |
| F | F | T | F | T |
APPEARS IN
RELATED QUESTIONS
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.
Angle is neither acute nor obtuse.
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:
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
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 following statement.
A quadratic equation has two distinct roots or 6 has three prime factors.
Write the truth value of the negation of the following statement.
London is in England.
Write the truth value of the negation of the following statement.
For every x ∈ N, x + 3 < 8.
Write the following statement in symbolic form.
If triangle is equilateral then it is equiangular.
Write the following statement in symbolic form.
Milk is white if and only if the sky is not blue.
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.
Neither 27 is a prime number nor divisible by 4.
If p and q are true and r and s are false, find the truth value of the following compound statement.
p ∧ (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) ∨ (r ∧ s)
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 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 a holiday and Ram studies on holiday.
If p : He swims
q : Water is warm
Give the verbal statement for the following symbolic statement:
p ↔ ~ q
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.
The Sun has set and Moon has risen.
Assuming the first statement p and second as q. Write the following statement in symbolic form.
Mona likes Mathematics and Physics.
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.
Kavita is brilliant and brave.
Assuming the first statement p and second as q. Write the following statement in symbolic form.
If Kiran drives the car, then Sameer will walk.
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.
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.
Rewrite the following statement without using conditional –
(Hint : p → q ≡ ∼ p ∨ q)
If price increases, then demand falls.
Write the negation of the following.
An angle is a right angle if and only if it is of measure 90°.
Rewrite the following statement without using the connective ‘If ... then’.
If a quadrilateral is rhombus then it is not a square.
Rewrite the following statement without using the connective ‘If ... then’.
If 10 − 3 = 7 then 10 × 3 ≠ 30.
Write the negation of the following statement.
I will have tea or coffee.
A biconditional statement is the conjunction of two ______ statements.
The negation of the statement (p ˄ q) `→` (r ˅ ∼ p) is ______.
State whether the following statement is True or False:
The converse of inverse of ~ p → q is q → ~ p
Negation of “Some men are animal” is ______.
If (p ∧ ~ r) → (~ p ∨ q) is a false statement, then respective truth values of p, q and r are ______.
Let p : 7 is not greater than 4 and q : Paris is in France by two statements. Then ∼(p ∨ q) is the statement ______
Which of the following is NOT true for p → q.
The logical statement (∼p → q) ∧ (q → p) is equivalent to: ______
Write the contrapositive of the inverse of the statement:
‘If two numbers are not equal, then their squares are not equal’.
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?
