Let, R = {(a, b): a,b andisin; Z and (a + b) is even}, then R isa)Reflexive relation on Zb)Equivalence relation on Zc)transitive relation on Zd)None of the aboveCorrect answer is option 'B'. Can you explain this answer?

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Let, R = {(a, b): a,b ∈ Z and (a + b) is even}, then R is

a)
Reflexive relation on Z
b)
Equivalence relation on Z
c)
transitive relation on Z
d)
None of the above

Correct answer is option 'B'. Can you explain this answer?

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Most Upvoted Answer

Let, R = {(a, b): a,b ∈ Z and (a + b) is even}, then R isa)Reflex...

Here, R = {(a, b): a,b ϵ Z and (a + b) is even}

Since,a + a = 2a, ,which is even, so R is reflexive.
If a + b is even then b + a will also be even. So, R is symmetric.
Let, a = 3, b = 5, and c = 7.

a + b = 3 + 5 = 8 (which is even), b + c = 5 + 7 = 12 (which is again even) and a + c = 3 + 7 = 10 (which is also even)
Therefore, R is an equivalence relation on Z.
Hence, option (2) is correct.

Answered by Engineers Club · View profile

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Let, R = {(a, b): a,b ∈ Z and (a + b) is even}, then R isa)Reflexive relation on Zb)Equivalence relation on Zc)transitive relation on Zd)None of the aboveCorrect answer is option 'B'. Can you explain this answer?

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