If A = {7, 8} and B = {2, 4, 6}, then A × B = {(7, 2), (7, 4), (7, 6), (8, 2), (8, 4), (8, 6)}TrueFalse

To determine if the statement is true or false, let's evaluate the Cartesian product $A \times B$ step by step.

1. ### Break Down the Problem

We need to calculate the Cartesian product of sets $A$ and $B$. The Cartesian product $A \times B$ is defined as the set of all ordered pairs $(a, b)$ where $a$ is an element from set $A$ and $b$ is an element from set $B$.

2. ### Relevant Concepts

The formula for the Cartesian product is: $A \times B = \{(a, b) | a \in A, b \in B\}$

3. ### Analysis and Detail

Given:

• $A = \{7, 8\}$
• $B = \{2, 4, 6\}$

Now, we will find all possible pairs:

• For $a = 7$:

  • $(7, 2)$
  • $(7, 4)$
  • $(7, 6)$

• For $a = 8$:

  • $(8, 2)$
  • $(8, 4)$
  • $(8, 6)$

Thus, the complete set of ordered pairs is: $A \times B = \{(7, 2), (7, 4), (7, 6), (8, 2), (8, 4), (8, 6)\}$

4. ### Verify and Summarize

The calculated Cartesian product matches the set mentioned in the question:

• The statement provided is indeed true as $A \times B$ equals $\{(7, 2), (7, 4), (7, 6), (8, 2), (8, 4), (8, 6)\}$.

Final Answer

True