Mark each statement True or False. Justify each answer. (a) If A ∩ B = ∅, then either A = ∅ or B = ∅. (b) If x ∈ A ∪ B, then x ∈ A or x ∈ B. (c) If x ∈ A \B, then x ∈ A or x ∉ B. (d) In proving S ⊆ T,...

Mark each statement True or False. Justify each answer.

(a) If A ∩ B = ∅, then either A = ∅ or B = ∅.

(b) If x ∈ A ∪ B, then x ∈ A or x ∈ B.

(c) If x ∈ A \B, then x ∈ A or x ∉ B.

(d) In proving S ⊆ T, one should avoid beginning with “Let x ∈ S,” because this assumes that S is nonempty.