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प्रश्न
If p → q is an implication, then the implication ∼ q → ∼ p is called its
पर्याय
Converse
Contrapositive
Inverse
Alternative
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उत्तर
Contrapositive
संबंधित प्रश्न
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.
Nagpur is in Maharashtra and Chennai is in Tamil Nadu.
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 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:
∼ (∼p ∧ ∼q) ∨ q
Construct the truth table of the following:
[(p ∧ q) ∨ r] ∧ [∼r ∨ (p ∧ q)]
Determine the truth values of p and q in the following case:
(p ∨ q) is T and (p ∧ q) is T
Write the truth value of the following statement.
Earth is a planet and Moon is a star.
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.
For every x ∈ N, x + 3 < 8.
If p and q are true and r and s are false, find the truth value of the following compound statement.
~ [(~ p ∨ s) ∧ (~ 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) ↔ ~(p ∨ q)
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 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
Assuming the first statement p and second as q. Write the following statement in symbolic form.
The necessary condition for existence of a tangent to the curve of the function is continuity.
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 Ram is tall and handsome.
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.
It is not true that the proof is lengthy but it is interesting.
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.
Ramesh is intelligent and he is hard working.
Write the negation of the following statement.
∃ x ∈ A, such that x + 5 < 11.
A biconditional statement is the conjunction of two ______ statements.
The negation of the statement (p ˄ q) `→` (r ˅ ∼ p) is ______.
Write the following statement in symbolic form:
Milk is white if and only if the sky is not blue.
Write the following statements in symbolic form
Even though it is not cloudy, it is still raining
Choose the correct alternative:
Negation of p → (p ˅ ~q) is
The symbolic form of the following circuit is (where p, q represents switches S1 and S2 closed respectively)
If c denotes the contradiction then the dual of the compound statement ∼p ∧ (q ∨ c) is ______
Let p : 7 is not greater than 4 and q : Paris is in France by two statements. Then ∼(p ∨ q) is the statement ______
The negation of the statement: "Getting above 95% marks is a necessary condition for Hema to get admission in good college'' is ______
The logical statement (∼p → q) ∧ (q → p) is equivalent to: ______
Write the converse, inverse, and contrapositive of the statement. "If 2 + 5 = 10, then 4 + 10 = 20."
Write the following statement in symbolic form.
It is not true that `sqrt(2)` is a rational number.
Write the following statement in symbolic form.
4 is an odd number if 3 is not a prime factor of 6.
The statement ∼(p ↔ ∼q) is ______.
Express the following compound statement symbolically:
Delhi is in India but Dhaka is not in Sri Lanka
Write the contrapositive of the inverse of the statement:
‘If two numbers are not equal, then their squares are not equal’.
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.
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?
