Question

I. Write True if the statement is correct, write False if the statement is in correct 1. If n(A)-20, n(B)-28 and n (A cup B)=36. then n ( A cap B)=12 2. If set A = \{1, 2\} and B = \{a, b\} then A x B = ((a, 1), (a, 2), (b, 1), (6, 2)) 3. An Empty set is a subset of every sets 4. For any two sets A and B are A*Delta*B =(A backslash B) cap(B backslash A) 5. For any two sets A and B are ( chi(B)' =A^ prime cap B^ prime

Answer 1

After evaluating each statement, the results are: the first statement is True, the second one is False, the third one is True, the fourth is False, and the fifth is True. These are basic set theory operations and properties used in high school mathematics.

Step-by-step explanation:

Let's evaluate each statement one by one:

1. If n(A) = 20, n(B) = 28 and n(A ∪ B) = 36, then n(A ∩ B) = 12. This statement can be evaluated using the principle of inclusion-exclusion for sets: n(A ∪ B) = n(A) + n(B) - n(A ∩ B). Let's substitute the given numbers and solve for n(A ∩ B): 36 = 20 + 28 - n(A ∩ B), thus n(A ∩ B) = 20 + 28 - 36 = 12. The statement is True.
2. If set A = \{1, 2\} and B = \{a, b\} then A x B = \{(1, a), (1, b), (2, a), (2, b)\}, not ((a, 1), (a, 2), (b, 1), (b, 2)). The elements are flipped in the given product. The statement is False.
3. An Empty set is a subset of every set. This statement is True because the definition of a subset includes the empty set as a subset of any set, including itself.
4. For any two sets A and B, A Δ B = (A \ B) ∪ (B \ A). This is the definition of the symmetric difference (Δ) of two sets. The statement as written, however, is incorrect because it uses the intersection operation (∩) instead of union (∪). Therefore, the statement is False.
5. For any two sets A and B, (A ∪ B)' = A' ∩ B'. This is an application of De Morgan's laws, which state that the complement of the union of two sets is the intersection of their complements. The statement is True.