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
Using the truth table, prove the following logical equivalence :
p ↔ q ≡ (p ∧ q) ∨ (~p ∧ ~q)
Evaluate: ∫ x . log x dx
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.
Nagpur is in Maharashtra and Chennai is in Tamil Nadu.
Write the following compound statement symbolically.
Angle is neither acute nor obtuse.
Construct the truth table of the following statement pattern.
p → [∼ (q ∧ r)]
Construct the truth table of the following statement pattern.
∼ p ∧ [(p ∨ ∼ q) ∧ q]
Write the truth value of the negation of the following statement.
`sqrt5` is an irrational number.
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.
Even though it is not cloudy, it is still raining.
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 : He swims
q : Water is warm
Give the verbal statement for the following symbolic statement.
q → p
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.
Rewrite the following statement without using conditional –
(Hint : p → q ≡ ∼ p ∨ q)
If price increases, then demand falls.
Write the negation of the following.
If ∆ABC is not equilateral, then it is not equiangular.
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.
I will have tea or coffee.
If (p ∧ ~ r) → (~ p ∨ q) is a false statement, then respective truth values of p, q and r are ______.
If p and q are true and rands are false statements, then which of the following is true?
The negation of the statement: "Getting above 95% marks is a necessary condition for Hema to get admission in good college'' is ______
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?
The statement ∼(p ↔ ∼q) is ______.
Express the following compound statement symbolically:
3 + 8 ≥ 12 if and only if 5 × 4 ≤ 25
