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Let A = {1, 2, 3, 4, 5, 6, 7} and B = {3, 6, 7, 9}. Then the number of elements in the set {C ⊆ A : C 
 B 
≠ 
Φ } is _________. (in integers)
Correct answer is '112'. Can you explain this answer?
Verified Answer
Let A = {1, 2, 3, 4, 5, 6, 7} and B = {3, 6, 7, 9}. Then the number of...
A = {1, 2, 3, 4, 5, 6, 7} and
B = {3, 6, 7, 9}
Total subset of A = 27 = 128
C ∩ B = φ when set C contains the element 1, 2, 4, 5.
 S = {C ⊆ A; C 
 B 
 Φ}
= Total – (C 
 B = Φ)
= 128 – 24 = 112
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Most Upvoted Answer
Let A = {1, 2, 3, 4, 5, 6, 7} and B = {3, 6, 7, 9}. Then the number of...

Explanation:

Given Sets:
- Set A = {1, 2, 3, 4, 5, 6, 7}
- Set B = {3, 6, 7, 9}

Find the set C:
- We need to find the set C that is a subset of A and has a non-empty intersection with set B.

Calculating the number of elements in C:
- The elements that are common between A and B are {3, 6, 7}.
- We can choose either 3, 6, or 7 to be in set C, which gives us 3 choices.
- For the remaining elements in set C, we can choose any element from the set A - {3, 6, 7}, which has 4 elements.
- So, the total number of elements in set C is 3 * 4 = 12.

Therefore, the number of elements in the set {C ⊆ A : C ∩ B ≠ ∅} is 12.
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Let A = {1, 2, 3, 4, 5, 6, 7} and B = {3, 6, 7, 9}. Then the number of elements in the set {C⊆A : C∩B≠Φ} is _________. (in integers)Correct answer is '112'. Can you explain this answer?
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