Answer:
a. Cat is the least popular.
b. It represents 8.
c. 6 people preferred giraffes than dogs.
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: 51
Step-by-step explanation:
let x be the number.
(70%)x = 42
0.7 x = 42
x = 60
we check 15% x 60 = 0.15 x 60 = 9, which is true.
85% of that number = 85% x 60 = 0.85 x 60 = 51.
Answer:
53 cm
Step-by-step explanation:
Using Pythagoras Theorem,
The hypotenuse
= 53 cm
