Question

check the relation R=A,A defined on the set A= { a,b} for the equivance relation.​

Answer 1

Answer:

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Answer 2

Answer:

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Step-by-step explanation:

A={x∈Z:0≤x≤12}={0,1,2,3,4,5,6,7,8,9,10,11,12}

R={(a,b):∣a−b∣is a multiple of 4}

For any element a∈A, we have (a,a)∈R as ∣a−a∣=0 is a multiple of 4.

∴R is reflexive.

Now, let (a,b)∈R⇒∣a−b∣ is a multiple of 4.

⇒∣−(a−b)∣=∣b−a∣ is a multiple of 4.

⇒(b,a)∈R

∴ is symmetric.

Now, let (a,b),(b,c)∈R

⇒∣a−b∣ is a multiple of 4 and ∣b−c∣ is a multiple of 4.

⇒(a−b) is a multiple of 4 and (b−c) is a multiple of 4.

⇒(a−c)=(a−b)+(b−c) is a multiple of 4.

⇒∣a−c∣ is a multiple of 4.

⇒(a,c)∈R.