## State which of the following sets are finite and which are infinite? (ii) B = {x :X EZ and x2 is even​}​

Question

State which of the following sets are finite and
which are infinite?
(ii) B = {x :X EZ and x2 is even​}​

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8 hours 2021-09-14T18:47:39+00:00 2 Answers 0 views 0

1. ) A = {X : X ∈ Z and x < 10}

= {….., -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9}

= {9, 8, 7, 6, 5, 4, 3, 2, 1, 0, -1, -2, -3, -4, …..}

∴ It is an infinite set.

(ii) B = {X : X ∈ W and 5x – 3 ≤ 20}

5x – 3 ≤ 20

⇒ 5x – 3 + 3 ≤ 20 + 3

⇒ 5x ≤ 20 + 3

⇒ 5x ≤ 23

⇒ x ≤ 23/5

(Dividing both sides by 5)

⇒ x ≤ 4.6

∴ B = {0, 1, 2, 3, 4}

∴ It is a finite set.

(iii) P = {y : y = 3x – 2, x ∈ N & x > 5}

When x = 6, y = 3 × 6 – 2

= 18 – 2 = 16

When x = 7, y = 3 × 7 – 2

= 21 – 2 = 19

When x = 8, y = 3 × 8 – 2

= 24 – 2

= 22

When x = 9, y = 3 × 9 -2

= 27 – 2

= 25

∴ P = {16, 19, 22, 25,…..}

∴ It is an infinite set.

(iv) M = {r : r = 3/n ; n ∈ W and 6 < n ≤ 15}

R = 3/n

When n= 7, r = 3/7

When n = 8, r = 3/8

When n = 9, r = 3/9

When n = 10, r = 3/10

When n = 11, r = 3/11

When n = 12, r = 3/12

When n = 13, r = 3/13

When n =14, r = 3/14

When n = 15, r = 3/15

∴ M = {3/7, 3/8, 3/9, 3/10, 3/11, 3/12, 3/13, 3/14, 3/15}

∴ It is a finite set.

finite

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