False — The statement is false because the left-hand side and right-hand side yield different values. Using the factorial notation from the context, 3! = 1 × 2 × 3 = 6 and 4! = 1 × 2 × 3 × 4 = 24, so 3! + 4! = 30. However, from Example 5 in the context, 7! = 5040. Since 30 ≠ 5040, the equality does not hold.

Is 3! + 4! = 7!?

Explanation

The statement is false because the left-hand side and right-hand side yield different values. Using the factorial notation from the context, 3! = $1 \times 2$ × 3 = 6 and 4! = $1 \times 2$ × $3 \times 4$ = 24, so 3! + 4! = 30. However, from Example 5 in the context, 7! = 5040. Since 30 $\neq$ 5040, the equality does not hold.

Solution Steps

Step 1: Calculate 3! = $1 \times 2$ × 3 = 6
Step 2: Calculate 4! = $1 \times 2$ × $3 \times 4$ = 24
Step 3: Find 3! + 4! = 6 + 24 = 30
Step 4: From the context, 7! = 5040
Step 5: Compare: 30 $\neq$ 5040, so the statement is False