Answer Step-by-step explanation:
Given statement if a-b is even and b-c is even then a-c is even .
Let p: a-b and b-c are even
q: a-c is even.
Converse: If a-c is even then a-b and b-c are both even.
Inverse:If a-b and b-c are not both even then a-c is not even.
If a= Even number
b= Even number
c=Even number
If a-c is even then a-b and b-c are both even..Hence, the converse statement is true.
If a=Odd number
b=Odd number
c= Odd number
If a-c is even then a-b and b-c are both even number .Hence, the converse statement is true.
If a=Even number
b= Even number
c= Odd number
a-b and b-c are both odd not even number but a-c is even number
a=8,b=6 c=3
a-b=8-6=2
b-c=6-3=3
a-c=8-3=5
If a-c is odd then a-b even but b-c is odd .Hence , the converse statement is false.But the inverse statement is true.
If a= Odd number
b=Even number
c= Even number
If a-b is odd and b-c is even then a-c is odd not even . Hence, the inverse statement is true.
If a= Odd number
b=Eve number
c=Odd number
a=9,b=6,c=5
a-b=9-6=3
b-c=6-5=1
a-c=9-5=4
Here, a-b and b-c are not both even but a-c is even .Hence, the inverse statement is false.
