Which of the following sets are equal? A = {x:x ∈ N, x < 3}, B = {

1.	Which of the following sets are equal? A = {x:x ∈ N, x < 3}, B = {1, 2}, C = {3, 1} D = {x : x ∈ N, x is odd, x < 5}, E = (1, 2, 1, 1}, F = {1, 1, 3}.
Answer» A = x is a natural number. And x is less than 3 So all natural numbers less than 3 constitute set A. {1, 2} A ={1, 2} B = {1, 2} C = {1, 3} D = x is a natural number. And x is less than 5 and is odd. So all odd natural numbers less than 5 constitute set D. {1, 3} D = {1, 3} E ={1, 2, 1, 1} We don’t repeat same elements in a set. ∴ E = {1, 2} F ={1, 1, 3} We don’t repeat same elements in a set. ∴ F = {1, 3} ∴ A = {1, 2} B = {1, 2} C = {1, 3} D = {1, 3} E = {1, 2} F = {1, 3} Now, we can see clearly that set A, B, E are equal and set C, D, F are equal.

Which of the following sets are equal? A = {x:x ∈ N, x < 3}, B = {1, 2}, C = {3, 1} D = {x : x ∈ N, x is odd, x < 5}, E = (1, 2, 1, 1}, F = {1, 1, 3}.

Answer»

A = x is a natural number. And x is less than 3

So all natural numbers less than 3 constitute set A.

{1, 2}

A ={1, 2}

B = {1, 2}

C = {1, 3}

D = x is a natural number. And x is less than 5 and is odd.

So all odd natural numbers less than 5 constitute set D.

{1, 3}

D = {1, 3}

E ={1, 2, 1, 1}

We don’t repeat same elements in a set.

∴ E = {1, 2}

F ={1, 1, 3}

We don’t repeat same elements in a set.

∴ F = {1, 3}

∴ A = {1, 2}

B = {1, 2}

C = {1, 3}

D = {1, 3}

E = {1, 2}

F = {1, 3}

Now, we can see clearly that set A, B, E are equal and set C, D, F are equal.