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Chapter 6: Q7. (page 218)

Use the conditional: If螖ABC is acute, then m鈭�C鈮�90.

Write the letter paired with the statement that is logically equivalent to 鈥淚f Dan can鈥檛 go, then Valerie can go.鈥�

  1. If Valerie can go, then Dan can鈥檛 go.
  2. If Dan can go, then Valerie can鈥檛 go.
  3. If Valerie can鈥檛 go, then Dan can go.
  4. If Dan can go, then Valerie can go.

Short Answer

Expert verified

The correct option is C.

Step by step solution

01

Step 1. Apply the concept of contrapositive.

To form the contrapositive of the conditional statement, interchange the hypothesis and the conclusion of the inverse statement.

02

Step 2. Step description.

A conditional and its contra positive are logically equivalent.

03

Step 3. Step description.

The contra positive of the statement is 鈥淚f Valerie can鈥檛 go, then Dan can go.鈥�

Hence, the correct option is c.

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