Question

Find the cardinal number of the following setsA1={-2,-1,1,3,5}​

Answer 1

Answer:

1. Clearly n(M) = 6

2. P = { 2, 5 , 8, 11, 14 }

since P contains 5 elements n(P) = 5

3.Q = {243, 768, 1875 }

since Q contains 3 elements n(Q) = 3

4.R = { -5, -4, -3, -2, -1, 0, 1, 2, 3, 4}

since R contains 10 elements n(R) = 10

5. S = { 1884, 1888, 1892, 1896, 1904}

since S contains 5 elements n(S) = 5

Step-by-step explanation:

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Answer 2

Answer:

Cardinal Number of a set: The number of elements in a set is called its Cardinal Number..

(i) A1 = {-2, -1, 1, 3, 5}

Cardinal number of set A1 = 5

(ii) A2 = {X : X ∈ N and 3 ≤   x < 7}

= {3, 4, 5, 6}

∴ Cardinal number of set A2 = 4

(iii) A3 = {P : P ∈ W and 2P – 3 < 8}

2P – 3 < 8

⇒ 2P – 3 + 3 < 8 + 3

(Adding 3 to both sides

⇒ 2P < 11

⇒ P < 11/2

(Dividing both sides by 2)

⇒ P < 5.5

∴ A3 = {0, 1, 2, 3, 4, 5}

∴ Cardinal number of set A3 = 6

(iv) A4 = {b : b ∈ Z and -7  < 3b -1 ≤ 2}

-7 < 3b – 1

⇒ -7 + 1 < 3b -1 + 1

(Adding 1 to both sides)

⇒ -6 < 3b

⇒ -(6/3) < b

(Dividing both sides by 3)

⇒ -2 < b

Again 3b – 1 ≤ 2

⇒ 3b – 1 + 1 ≤ 2 + 1

(Adding 1 to both sides)

⇒ 3b ≤ 3

⇒ b ≤ 3/3

(Dividing both sides by 3)

⇒ b ≤ 1

∴ -2 < b ≤ 1

∴ Given set A4 = {-1, 0, 1}

∴ Cardinal number of set A4 = 3