MTH202 Assignment no 2 Spring 2013 Idea Solution written update
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.” Marks = 5
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. Marks = 3
(ii) Use the above sets A, B and C to verify the identity
(A – B) – C = (A – C) – B Marks = 3+3+1
Q3: Let A = { 2, 3, 4, 5, 6, 7, 8}.
Define a relation R on A as for xRy x divides y.
(i) Write the relation R in tabular form
(ii) Determine whether the relation is reflexive or not. Marks = 2 + 3
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.
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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.
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