74. Asked if you will cast your vote for a party the following feedback is obtained: - Adult Male Adult Female Youth over 18 years Yes No Don't know 10 20 5 20 15 5 10 5 10 If A = set of Adult C = Common set of Women and Youth Y = set of positive opinion N = set of negative opinion then n(A') is (a) 25 (b) 40 10+5+10 = 25 (c) 20 (d) None 75. As per question No. (74) with the same order of options (a), (b), (c) and (d) the set n(A ∩ C) is 76. As per question No. (74) with the same order of options (a), (b), (c) and (d) the set n(Y∪N)' is 5+5+10 = 20 77. As per question No. (74) with the same order of options (a), (b), (c) and (d) the set n[A ∩ (Y∪N)'] isSee answer

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74 Asked if you will cast your vote for a party the following feedback is obtained Adult Male Adult Female Youth over 18 years Yes No Dont know 10 20 5 20 15 5 10 5 10 If A set of Adult C Common set…

Question

74. Asked if you will cast your vote for a party the following feedback is obtained: –
Adult Male
Adult Female
Youth over 18 years
Yes
No
Don’t know
10
20
5
20
15
5
10
5
10
If A = set of Adult C = Common set of Women and Youth Y = set of positive opinion N = set of negative opinion then n(A’) is
(a) 25
(b) 40
10+5+10 = 25
(c) 20
(d) None
75. As per question No. (74) with the same order of options (a), (b), (c) and (d) the set n(A ∩ C) is
76. As per question No. (74) with the same order of options (a), (b), (c) and (d) the set n(Y∪N)’ is 5+5+10 = 20
77. As per question No. (74) with the same order of options (a), (b), (c) and (d) the set n[A ∩ (Y∪N)’] is

Basic Answer

Let’s break down the questions step by step.

Question 74:

Given:

• Adult Male: 10 Yes, 20 No, 5 Don’t know
• Adult Female: 20 Yes, 15 No, 5 Don’t know
• Youth over 18 years: 10 Yes, 5 No, 10 Don’t know

Sets:

• A = Set of Adults
• C = Common set of Women and Youth
• Y = Set of positive opinion (Yes)
• N = Set of negative opinion (No)

Find:

• n(A’)

Step 1: Calculate Total Adults

• Adult Male: 10 + 20 + 5 = 35
• Adult Female: 20 + 15 + 5 = 40

Total Adults (A) = 35 + 40 = 75

Step 2: Calculate Total Individuals

• Adult Male: 35
• Adult Female: 40
• Youth over 18 years: 10 + 5 + 10 = 25

Total Individuals = 35 + 40 + 25 = 100

Step 3: Calculate n(A’)

n(A’) = Total Individuals – n(A)
n(A’) = 100 – 75 = 25

Final Answer

(a) 25

Question 75:

Find:

• n(A ∩ C)

Step 1: Identify A and C

• A = Set of Adults
• C = Common set of Women and Youth

Step 2: Calculate n(A ∩ C)

• A includes both Adult Male and Adult Female
• C includes Adult Female and Youth over 18 years

Common elements in A and C are Adult Female.

n(A ∩ C) = 40 (Adult Female)

Final Answer

(b) 40

Question 76:

Find:

• n(Y ∪ N)’

Step 1: Calculate n(Y)

• Y = Set of positive opinion (Yes)
• Y = 10 (Adult Male) + 20 (Adult Female) + 10 (Youth) = 40

Step 2: Calculate n(N)

• N = Set of negative opinion (No)
• N = 20 (Adult Male) + 15 (Adult Female) + 5 (Youth) = 40

Step 3: Calculate n(Y ∪ N)

• Y ∪ N = 40 (Yes) + 40 (No) = 80

Step 4: Calculate n(Y ∪ N)’

• n(Y ∪ N)’ = Total Individuals – n(Y ∪ N)
• n(Y ∪ N)’ = 100 – 80 = 20

Final Answer

(c) 20

Question 77:

Find:

• n[A ∩ (Y ∪ N)’]

Step 1: Calculate n(Y ∪ N)’

• Already calculated in Question 76: n(Y ∪ N)’ = 20

Step 2: Calculate n[A ∩ (Y ∪ N)’]

• A = Set of Adults = 75
• (Y ∪ N)’ = 20

Common elements in A and (Y ∪ N)’ are those who are Adults and have neither a positive nor a negative opinion.

n[A ∩ (Y ∪ N)’] = 20 (Don’t know)

Final Answer

(c) 20