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​}​

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

Answers ( )

    0
    2021-09-14T18:48:53+00:00

    ) 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

    (Adding 3 to both sides)

    ⇒ 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.

    0
    2021-09-14T18:49:05+00:00

    Answer:

    finite

    Step-by-step explanation:

    n Jen

    h hero

    Jedi

Leave an answer

Browse
Browse

18:9+8+9*3-7:3-1*13 = ? ( )