Advertisements
Advertisements
Question
Rewrite the following statement without using the connective ‘If ... then’.
If 10 − 3 = 7 then 10 × 3 ≠ 30.
Advertisements
Solution
Let p : 10 − 3 = 7
q : 10 × 3 ≠ 30
The given statement is p → q.
But p → q ≡ ~p ∨ q.
∴ The given statement can be written as
'10 - 3 ≠ 7 or 10 × 3 ≠ 30'.
APPEARS IN
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 that p ↔ q = (p ∧ q) ∨ (~p ∧ ~q).
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) is T
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 negation of the following statement.
All men are animals.
Find the truth value of the following statement.
Every accountant is free to apply his own accounting rules if and only if machinery is an asset.
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 and q are true and r and s are false, find the truth value of the following compound statement.
[(p ∨ s) → r] ∨ ~ [~ (p → q) ∨ s]
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)
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
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.
An angle is a right angle if and only if it is of measure 90°.
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.
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 it rains then the principal declares a holiday.
Without using truth table show that -
(p ˅ q) ˄ (∼p v ∼q) ≡ (p ∧ ∼q) ˄ (∼p ∧ q)
Choose the correct alternative:
A biconditional statement is the conjunction of two ______ statements
Negation of “Some men are animal” is ______.
The Boolean expression ∼(q ⇒ ∼p) is equivalent to: ______
The statement, 'If I go to school, then I will get knowledge' is equivalent to ______
Converse of the statement q `rightarrow` p is ______.
Using the statements
p: Seema is fat,
q: Seema is happy,
Write the following statements in symbolic form;
- Seema is thin and happy.
- If Seema is fat then she is unhappy.
