Q50. - Algebra 1

Question

Explain how deductive reasoning is used to show that a conditional is true or false.

Step-by-Step Solution

Answer

Deductive reasoning can be used to show that a conditional is true or false by checking if the conclusion is true or false when the hypothesis is true.

Step 1. State the concept.

The process of using facts, rules, definitions, or properties to reach a valid conclusion is called deductive reasoning.

Step 2. List the different cases.

A conditional is a conditional statement that contains two parts: hypothesis and conclusion.

Case 1: Hypothesis is true and Conclusion is true

In this case, the conditional is said to be true.

Case 2: Hypothesis is true and Conclusion is false

In this case, the conditional is said to be false.

Case 3: Hypothesis is false and Conclusion is true

In this case, the conditional is said to be true.

Case 4: Hypothesis is false and Conclusion is false

In this case, the conditional is said to be true.

Step 3. To determine if a conditional is true.

Deductive reasoning can be used to check if a conditional is true or false. Assume some conditions for which the hypothesis is true. If the conclusion can be shown to be true for all such conditions, then the conditional is true. Otherwise, if there is a condition for which the hypothesis is true but the conclusion is false, then the conditional is false.