Q1: Write the conditional, biconditional, inverse, converse, and contra-positive statements of the following:

p = “You are a truthful and honest person.”
q = “People like and respect you.”
Solution:
Conditional:
If you are a truthful and honest person then people like and respect you.
Biconditional:
You are a truthful and honest person if and only if people like and respect you.
Inverse:
If you are not a truthful and honest person then people do not like and respect you.
Converse:
If people like and respect you then you are a truthful and honest person.
Contra Positive:
If people do not like and respect you then you are not a truthful and honest person.



Q2: Given
A = Set of first 5 prime numbers
B = Set of first 5 natural numbers
C = Set of first 5 odd natural numbers

(i) Write the given sets A, B and C into Tabular form.
(ii) Use the above sets A, B and C to verify the identity
(A – B) – C = (A – C) – B
Solution:
(i) write the given sets A, B and C into Tabular form
A= {1, 2, 3, 5, 7}
B= {1, 2, 3, 4, 5}
C= {1, 3, 5, 7, 9}
(ii) Use the sets A, B and C to verify the identity

(A – B) – C = (A – C) – B
A={1,2,3,5,7}

B={1,2,3,4,5}

C={1,3,5,7,9}
A-B= {1, 2, 3, 5, 7}-{1, 2, 3, 4, 5}
= {5, 7}
(A – B) – C = {5, 7}-{1, 3,5 ,7,9}
= { } ...................... (1)
(A – C) ={1,2,3,5,7} - {1,3,5,7,9}
= {2}
(A – C) – B= {2} - {1, 2, 3, 4, 5}
= { } ........................ (2
(A – B) – C = (A – C) – B
{ }={ }
So (A – B) – C = (A – C) – B.