We are to show that if X ⊆ Y then (X ∪ Z) ⊆ (Y ∪ Z) for sets X, Y, Z.
Assume that a is a representative element of X, that is, a ∈ X. By the definition of union, a ∈ X ∪ Z. Now because X ⊆ Y and we assumed a ∈ X, then a ∈ Y by the definition of subset. And because a ∈ Y, then a ∈ Y ∪ Z by definition of union.
We chose our representative element, a, and showed that a ∈ X ∪ Y implies that a ∈ Y ∪ Z and this completes the proof.
Answer:
∠ QPR = 56°
Step-by-step explanation:
Δ RST is isosceles ( 2 congruent sides ) , then base angles are congruent
∠ SRT =
=
= 68°
∠ PRQ and ∠ SRT are vertically opposite angles and are congruent , so
∠ PRQ = 68°
Δ PRQ is isosceles ( 2 congruent sides ), then base angles are congruent , so
∠ QPR =
=
= 56°
Yes this is arithmetic; the next two sequences would follow the pattern: 4x+2 and 5x+2
Answer:
See Explanation
Step-by-step explanation:
See attachment for complete question.
From the attachment, we have that:



First, we calculate the total



Solving (a): Probability of A
This is calculated using:



Solving (b): Probability of C
This is calculated using:



Solving (b): Probability of T
This is calculated using:


