Questions: Determine the truth value for each simple statement. Then use these truth values to determine the truth value of the compound statement. 8+7=22-5 and 50+5=3 * 3 The simple statement 9+7=22-5 is false. The simple statement 50+5=3 * 3 is

Determine the truth value for each simple statement. Then use these truth values to determine the truth value of the compound statement. 8+7=22-5 and 50+5=3 * 3 The simple statement 9+7=22-5 is false. The simple statement 50+5=3 * 3 is
Transcript text: Determine the truth value for each simple statement. Then use these truth values to determine the truth value of the compound statement. $8+7=22-5$ and $50+5=3 \cdot 3$ The simple statement $9+7=22-5$ is false. The simple statement $50+5=3 \cdot 3$ is $\square$
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Solution

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Solution Steps

To determine the truth value of the compound statement, evaluate each simple statement individually. The compound statement is true only if both simple statements are true.

  1. Evaluate the truth of the statement \(8+7=22-5\).
  2. Evaluate the truth of the statement \(50+5=3 \cdot 3\).
  3. Use the truth values of the simple statements to determine the truth value of the compound statement using the logical "and".
Step 1: Evaluate the First Simple Statement

Evaluate the truth of the statement \(8 + 7 = 22 - 5\).

  • Calculate \(8 + 7 = 15\).
  • Calculate \(22 - 5 = 17\).
  • Since \(15 \neq 17\), the statement is false.
Step 2: Evaluate the Second Simple Statement

Evaluate the truth of the statement \(50 + 5 = 3 \cdot 3\).

  • Calculate \(50 + 5 = 55\).
  • Calculate \(3 \cdot 3 = 9\).
  • Since \(55 \neq 9\), the statement is false.
Step 3: Determine the Truth Value of the Compound Statement

The compound statement is \(8 + 7 = 22 - 5\) and \(50 + 5 = 3 \cdot 3\).

  • The compound statement is true only if both simple statements are true.
  • Since both statements are false, the compound statement is false.

Final Answer

The truth value of the compound statement is \(\boxed{\text{False}}\).

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