Fundamentals of Math

Fundamentals of Mathematics

Practice 8.2

Directions: Write the converse, the inverse, and the contrapositive of the conditional statements given and then state whether each new statement is true or false.

1. Conditional: If you live in Washington, D.C., then you live in the capital of the United States. a. Converse:

b. Inverse:

c. Contrapositive:

2. Conditional: If today is Friday, then tomorrow is Saturday. a. Converse:

b. Inverse:

c. Contrapositive:

3. Conditional: If a number is an Integer, then it is also a Real number. a. Converse:

b. Inverse:

c. Contrapositive:

Answer Key on Page 126

8.3 Counterexamples In math, proving conditional, biconditional, converse, inverse, or contrapositive statements can be a bit challenging. This is because proving mathematical statements true requires a formal proof. However, showing that a mathematical statement is false is much easier. All that's needed to prove a statement false is to provide a single statement that goes against the statement's conclusion, a counterexample . For example, we can disprove the statement "all birds can fly" by offering an example of a bird that cannot fly - penguins.

Practice 8.3

Directions: Provide a counterexample to each statement given below.

1. If it is a printed book, then it will contain pictures inside. 2. The sum of + 2 is always equal to 3. 3. If a number is divisible by 2, then it is a multiple of 4.

Answer Key on Page 126

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