Question
Question: Write the contrapositive or converse of the following statements: A) If \(x\) is a prime number th...
Write the contrapositive or converse of the following statements:
A) If x is a prime number then x is odd.
B) If the two lines are parallel then they do not intersect in the same plane.
C) Something is cold implies that it has low temperature.
D) You can’t comprehend geometry if you don’t know how to reason deductively
E) x is an even number implies that x is divisible by 4
Solution
According to given in the question we have to find the contrapositive or converse of all the given statements:
First of all we have to understand about the prime numbers so a prime number is a natural number which is greater than 1 and is not a product of two smaller number numbers. Or the number which is divisible by 1 or itself is known as the prime number.
Now, we have to understand about the odd numbers so, an number or integer that can’t be divisible by 2 is known as the odd number as (1,3,5,7,......)
Now, we have to understand about the even numbers so, an number or integer that can’t be divisible by 3 is known as the odd number as (2,4,6,8,......)
Complete step-by-step answer:
Step 1: First of all we have to find the contrapositive or converse of (i) If x is a prime number then x is odd.
Contrapositive when x is a prime number then x is odd is as follows: If the number x is odd then x is not a prime number.
Converse of x is a prime number then x is odd is as follows: if a number x is odd then it is a prime number.
Step 2: Now, we will find the contrapositive or converse of (ii) If the two lines are parallel then they do not intersect in the same plane.
Contrapositive of If the two lines are parallel then they do not intersect in the same plane is as follows: If two lines intersect in the same plane then they are not parallel.
Conversely If the two lines are parallel then they do not intersect in the same plane as follows: If two lines do not intersect in the same plane then they are parallel.
Step 3: Now, we will find the contrapositive or converse of (iii) Something is cold implies that it has low temperature.
Contrapositive of Something is cold implies that it has low temperature is as follow: If sometimes does not have low temperature then it is not cold.
Converse of Something is cold implies that it has low temperature is as follows: If something is at low temperature then it is cold.
Step 4: Now, we will find the contrapositive or converse of (iv) You can’t comprehend geometry if you don’t know how to reason deductively.
Contrapositive of You can’t comprehend geometry if you don’t know how to reason deductively is as follow: If you don’t know how to reason deductively then you can comprehend geometry.
Conversely, You can’t comprehend geometry if you don’t know how to reason deductively is as follows: If you don’t know how to reason deductively then you can’t comprehend geometry.
Step 5: Now, we will find the contrapositive or converse of (v) x is an even number implies that x is divisible by 4.
Contrapositive of x is an even number implies that x is divisible by 4 is as follows: If x is not divisible by 4 then x is not an even number.
Converse of x is an even number implies that x is divisible by 4 is as follows: If x is divisible by 4 then x is an even number.
Note: A proposition or theorem formed by contradicting both the subject and predicate or both the hypothesis and conclusion of a given proposition or theorem and interchanging them is known as contrapositive.
The converse of a statement is the result of reversing of it’s two constituent statements.