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Two finite sets have p and q number of elements. The total number of subsets of first set is eight times the total number of subsets of the second set. Find the of p-q. a) 2 b) 3 c)4 d) None of the above The answer is B explain how?
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Two finite sets have p and q number of elements. The total number of s...
Explanation:

Let's assume that the two given sets are A and B.

Step 1: Find the number of subsets for set B
The number of subsets for any finite set with q elements is given by 2^q.
Therefore, the number of subsets for set B is 2^q.

Step 2: Find the number of subsets for set A
The total number of subsets for set A is given by 2^p.

Step 3: Use the given information to form an equation
The problem states that the total number of subsets for set A is eight times the total number of subsets for set B. Therefore, we can form the following equation:
2^p = 8 * 2^q

Step 4: Simplify the equation
We can simplify the equation as follows:
2^p = 2^3 * 2^q
2^p = 2^(q+3)

Step 5: Solve for p-q
Since we want to find the value of p-q, we can take the logarithm of both sides of the equation with base 2:
p = q + 3
p - q = 3

Therefore, the value of p-q is 3. The correct option is (b).
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Two finite sets have p and q number of elements. The total number of subsets of first set is eight times the total number of subsets of the second set. Find the of p-q. a) 2 b) 3 c)4 d) None of the above The answer is B explain how?
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