A − (B ∪ C) = (A − B) − C.(3 marks)(b) Consider the sets S = {3, 5} and T = {2, 3, 7}. Indicate whether each of the followingstatements is true or false; no explanation is needed.(2 marks)(i) S ⊆ T(ii) ∅ ∈ P(S)(iii) ∅ ∈ T(iv) (3, 3, 3) ∈ S × T
Question
A − (B ∪ C) = (A − B) − C.(3 marks)(b) Consider the sets S = {3, 5} and T = {2, 3, 7}. Indicate whether each of the followingstatements is true or false; no explanation is needed.(2 marks)(i) S ⊆ T(ii) ∅ ∈ P(S)(iii) ∅ ∈ T(iv) (3, 3, 3) ∈ S × T
Solution
(a) A − (B ∪ C) = (A − B) − C.
This statement is true. Here's how:
Step 1: B ∪ C means the union of sets B and C, which includes all elements that are in B, or in C, or in both.
Step 2: A - (B ∪ C) means the set of elements that are in A but not in the union of B and C.
Step 3: (A - B) means the set of elements that are in A but not in B.
Step 4: (A - B) - C means the set of elements that are in A, not in B, and also not in C.
So, A - (B ∪ C) is the same as (A - B) - C.
(b) Consider the sets S = {3, 5} and T = {2, 3, 7}.
(i) S ⊆ T
This statement is false. S is not a subset of T because 5 is in S but not in T.
(ii) ∅ ∈ P(S)
This statement is true. The power set P(S) includes all subsets of S, including the empty set ∅.
(iii) ∅ ∈ T
This statement is false. The empty set ∅ is not an element of T.
(iv) (3, 3, 3) ∈ S × T
This statement is false. The Cartesian product S × T includes all ordered pairs (s, t) where s is in S and t is in T. The triplet (3, 3, 3) is not included because it's not a pair and 3 is not in T twice.
Similar Questions
1） Use the logical equivalences below and the definitions of set operations to prove, or provide a counterexample to disprove, the following set identity: (A ∪ B) ∖ C = (A ∖ C) ∪ (B ∖ C) 2）Use the logical equivalences below and the definitions of set operations to prove, or provide a counterexample to disprove, the following set identity: (A ∪ B) ∖ C = (A ∖ C) ∪ B
4. Let A and B be sets. Show thata) (A ∩ B) ⊆ A b) A ⊆ (A ∪ B) c) A − B ⊆ Ad) A ∩ (B − A) = ∅ e) A ∪ (B − A) = A ∪ B f) A ⊕ B = (A ∪ B) − (A ∩ B).
Select the set that is equivalent to (S∪T)\(S ∩ -T). a.S ∪ T b.T c.S d.S ∩ T
U = {a, b, c, d, e} A = {d, e} B = {a, b, c}.Which one of the following statements regarding the given sets is FALSE?a.A’ – U = {d, e}b.(A ⋂ B) + U = {a, b, c, d, e}c.(U ⋂ B’) = B’d.(U – A) + B = U – (A + B)
U = {1, 2, {1}, {2}, {1, 2}} A = {1, 2, {1}} B = {{1}, {1, 2}} C = {2, {1}, {2}}.Which one of the following statements is valid if x ∉ B U C? (Hint: Determine U – (B U C).)a.x ∈ {1}.b.x ∈ ⊘.c.x ∈ {1, 2}.d.x ∈ B and x ∈ C.
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.