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Let R be a relation on a collection of sets defined as follows,

R=(A,B)

   Then pick out the correct statement(s).

1) R is reflexive and transitive

2) R is symmetric

3) R is antisymmetric.

4) R is reflexive but not transitive​

User Brutasse
by
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1 Answer

2 votes

Answer:

Options 1) and 3) are correct.

Explanation:

R=(A,B)

Reflexive:

As A⊆A,
(A,A)∈ R.

So, R is reflexive

Symmetric:

Let
(A,B)∈ R. So, A⊆B

Take
A=\{1,2\}\,,\,B=\{1,2,3,4\}

Here, A⊆B but B⊄A

So,
(B,A)∉ R

R is not symmetric

Transitive:

Let
(A,B)∈ R and
(B,C)∈ R

So, A⊆B and B⊆C.

Therefore, A⊆C

So,


(A,C)∈ R

Hence, R is transitive.

Option 1) is correct.

Antisymmetric:

Let (A,B)∈R and (B,A)∈R

So, A⊆B and B⊆A

Hence, A = B

So, R is antisymmetric

Option 3) is also correct.

User LEQADA
by
8.0k points
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