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Question
Let R be a relation from N to N defined by R = {(a, b) : a, b ∈ N and a = b2}. Is the statement true?
(a, b) ∈ R and (b, c) ∈ R implies (a, c) ∈ R
Justify your answer in case.
Options
True
False
Solution
This statement is False.
Explanation:
Given: R = [(a, b) : a, b ∈ N and a = b2]
(a, b) ∈ R and (b, c) ∈ R ⇒ (a, c) ∈ R
∵ 16 = 42 and 4 = 22
∴ (16, 4) ∈ R and (4, 2) ∈ R
Here,
(16, 2) ∉ R
(a, b) ∈ R and (b, c) ∈ R but (a, c) ∉ R.
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