Question

State, if the following pair of a set is equal or not :

M = {x : x ∈ W and x + 3 < 8} and N = {y : y = 2n -1, n ∈ N and n < 5}

Answer 1

M = {x : x ∈ W and x + 3 < 8}

x + 3 < 8

⇒ x < 8 - 3

⇒ x < 5

∴ M = {0, 1,2, 3, 4}

N = {y : y = 2n -1, n ∈ N and n < 5}

y = 2n - 1

When n = 1,
y = 2 x 1-1
⇒ y = 2-1
= 1

When n = 2,
y = 2 x 2-1
⇒ y = 4-1
= 3

When n =3,
y = 2 x 3-1
⇒ y = 6-1
= 5

When n = 4,
y = 2 x 4-1
⇒ y = 8-1
= 7

∴ N = {1, 3, 5,7}

Now we see that elements of sets M and N are not the same (identical)

∴ Sets M and N are not equal.