Question

1. choose the number that is the intersection of sets a and b.

a = {5,10,15,20,25,30...}
b = {1,3,5,7,9,11,13}
a∩b = {10}
a∩b = {5,15}
a∩b = {5}
a∩b = {3}

Explanation:

Step1: Recall intersection definition

The intersection of two sets \( A \) and \( B \), denoted \( A \cap B \), is the set of elements that are in both \( A \) and \( B \).

Step2: Identify elements in both sets

Set \( A = \{5, 10, 15, 20, 25, 30, \dots\} \) (multiples of 5) and set \( B = \{1, 3, 5, 7, 9, 11, 13\} \). Check each element of \( B \) in \( A \):

• \( 1 \): Not in \( A \) (since \( A \) has multiples of 5).
• \( 3 \): Not in \( A \) (not a multiple of 5).
• \( 5 \): In \( A \) (5 is a multiple of 5).
• \( 7 \): Not in \( A \).
• \( 9 \): Not in \( A \).
• \( 11 \): Not in \( A \).
• \( 13 \): Not in \( A \).

So the only element common to both \( A \) and \( B \) is \( 5 \).

Answer:

\( A \cap B = \{5\} \) (the option corresponding to this is the one with \( A \cap B = \{5\} \))