Final answer:
To find the intersection, union, and difference of sets (A x B) and (B x B), and the cross product of (A ∩ B) and A, we need to apply set operations. The notation (N в) is unknown and the intersection and difference of power sets can be found accordingly.
Step-by-step explanation:
(a) (A x B) ∩ (B x B)
To find the intersection of two sets, we need to find the elements that are common to both sets.
Using the given sets, (A x B) = {(b,a), (c,b), (d,a)} and (B x B) = {(a,a), (b,b)}.
Therefore, the intersection of (A x B) and (B x B) is {(b,a), (b,b)}.
(b) (A x B) u (B x B)
To find the union of two sets, we need to combine all the elements from both sets without duplicates.
Using the given sets, (A x B) = {(b,a), (c,b), (d,a)} and (B x B) = {(a,a), (b,b)}.
Therefore, the union of (A x B) and (B x B) is {(b,a), (c,b), (d,a), (a,a), (b,b)}.
(c) (A x B) - (B x B)
To find the difference of two sets, we need to remove any elements from the first set that are also in the second set.
Using the given sets, (A x B) = {(b,a), (c,b), (d,a)} and (B x B) = {(a,a), (b,b)}.
Therefore, the difference of (A x B) and (B x B) is {(c,b), (d,a)}.
(d) (A ∩ B) x A
To find the cross product of two sets, we need to pair each element from the first set with each element from the second set.
Using the given sets, (A ∩ B) = {b} and A = {b, c, d}.
Therefore, the cross product of (A ∩ B) and A is {(b,b), (b,c), (b,d)}.
(e) (A x B) N в
Sorry, but the provided notation (N в) is unknown. Can you please provide more information or clarify?
(f) P(A) N P(B)
To find the intersection of two sets, we need to find the elements that are common to both sets.
Using the given sets, P(A) represents the power set of A, and P(B) represents the power set of B.
Therefore, the intersection of P(A) and P(B) would be the set of all subsets that are common to both sets.
(g) P(A) - P(B)
To find the difference of two sets, we need to remove any elements from the first set that are also in the second set.
Using the given sets, P(A) represents the power set of A, and P(B) represents the power set of B.
Therefore, the difference of P(A) and P(B) would be the set of all subsets that are in P(A) but not in P(B).
Complete question:
Suppose A = {b, c, d} and B = {a,b}. Find:
(a) (A x B) ∩ (B x B)
(b) (A x B) u (B x Β)
(c) (A x B) - (B x B)
(d) (A ∩ B) x A
(e) (A x B) N в
(f) P(A) N P(B)
(g) P(A) - P(B)