Let R be a relation on a collection of sets defined as follows, R={(A, B)|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

Options 1) and 3) are correct.

Step-by-step explanation:

R={(A,B)|A⊆B}

Reflexive:

As A⊆A,  ∈ R.

So, R is reflexive

Symmetric:

Let ∈ R. So, A⊆B

Take

Here, A⊆B but B⊄A

So, ∉ R

R is not symmetric

Transitive:

Let ∈ R and ∈ R

So, A⊆B and B⊆C.

Therefore, A⊆C

So,

∈ 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.

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step-by-step explanation:

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