Advertisements
Advertisements
Question
The contrapositive of the statement “If p, then q”, is ______.
Options
If q, then p
If p, then ~ q
If ~ q, then ~ p
If ~ p, then ~ q
Solution
The contrapositive of the statement “If p, then q”, is if ~ q, then ~ p.
Explanation:
Here the statement is “If p, then q”
i.e. p → q
Contrapositive of the statement p → q is (~ q) → (~ p)
i.e., If ~ q, then ~ p.
APPEARS IN
RELATED QUESTIONS
Write the contrapositive and converse of the following statements.
If x is a prime number, then x is odd
Write the contrapositive and converse of the following statements.
It the two lines are parallel, then they do not intersect in the same plane.
Write the contrapositive and converse of the following statements.
You cannot comprehend geometry if you do not know how to reason deductively.
Write each of the following statement in the form “if-then”.
You get a job implies that your credentials are good.
State the converse and contrapositive of each of the following statements:
q: I go to a beach whenever it is a sunny day.
State the converse and contrapositive of each of the following statements:
r: If it is hot outside, then you feel thirsty.
Re write each of the following statements in the form “p if and only if q”.
q: For you to get an A grade, it is necessary and sufficient that you do all the homework regularly.
Given below are two statements
p: 25 is a multiple of 5.
q: 25 is a multiple of 8.
Write the compound statements connecting these two statements with “And” and “Or”. In both cases check the validity of the compound statement.
State the converse and contrapositive of statement:
If it is hot outside, then you feel thirsty.
Determine the contrapositive of the statement:
If it snows, then they do not drive the car.
Determine the contrapositive of the statement:
It never rains when it is cold.
Determine the contrapositive of the statement:
If Ravish skis, then it snowed.
Determine the contrapositive of the statement:
If x is less than zero, then x is not positive.
Determine the contrapositive of the statement:
Only if he does not tire will he win.
Check whether the statement are true or not:
p : If x and y are odd integers, then x + y is an even integer.
Show that the following statement is true.
p: For any real numbers x, y if x = y, then 2x + a = 2y + a when a ∈ Z.
Write down the contrapositive of the following statements:
If x and y are negative integers, then xy is positive.
Write down the contrapositive of the following statements:
If it snows, then the weather will be cold.
Write down the converse of following statements:
If a rectangle ‘R’ is a square, then R is a rhombus.
Write down the converse of following statements:
If you go to Agra, then you must visit Taj Mahal.
Write down the converse of following statements:
If x : y = 3 : 2, then 2x = 3y.
Write down the converse of following statements:
If two triangles are similar, then the ratio of their corresponding sides are equal.
Using contrapositive method prove that if n2 is an even integer, then n is also an even integers.
The contrapositive of the statement “If 7 is greater than 5, then 8 is greater than 6” is ______.
Write the statement in the form “if p, then q”.
p: It is necessary to have a password to log on to the server.
