Question

Write the steps on the left to their corresponding step number on the right to prove the given statement.

(A ∩ B) ⊆ A
Thus x is in A.
If x is in A
then x is in An B.
x is in A and x is in B by definition of intersection.

Answer 1

To prove the statement (A ∩ B) ⊆ A, we can use the definition of intersection and the properties of sets.

Step-by-step explanation:

To prove the statement (A ∩ B) ⊆ A, we need to show that for any x in (A ∩ B), x must also be in A.

To prove this, we can use the definition of intersection. Let's assume x is in (A ∩ B). This means x is in both A and B.

1. By definition of intersection, x is in A
2. Since x is in A, x is in A and B by definition of intersection
3. Therefore, x is in A

Thus, we have proven that if x is in (A ∩ B), then x is in A.