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Chapter 2: Q7 (page 34)

State the hypothesis and the conclusion of each conditional.

Combine the conditionals in Exercises 5 and 6 into a single biconditional.

Short Answer

Expert verified

The biconditional of both the statements is 鈥�if and only if 鈥�.

Step by step solution

01

Step 1. Define the biconditional.

If a conditional and its converse are both true then they can be combined into a single statement by using connector 鈥渋f and only if鈥�. Such a statement containing the words 鈥渋f and only if鈥� is defined as a biconditional. For example, 鈥�p if and only if q鈥�.

02

Step 2. Rewrite the statements.

The given statement 鈥� if 鈥� can be rewritten as 鈥淚f , then 鈥�.

The given statement 鈥� only if 鈥� can be rewritten as 鈥淚f , then 鈥�.

03

Step 3. Write the biconditional.

The biconditional would be 鈥�if and only if 鈥�.

Therefore, the biconditional of both the statements is 鈥�if and only if 鈥�.

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Most popular questions from this chapter

Justify each step.

z+73=鈭�11

z+7=鈭�33

z=鈭�40

Tell whether each statement is true or false. Then write converse and tell whether it is true or false.

Statement: If x=鈭�6,thenx=6.

Justify each statement with a property from algebra or property of congruence.

2a+b=2a+2b

State which postulate, definition, or theorem justifies the statement about the diagram.

m鈭�AEB+m鈭�BEC=m鈭�AEC

Tell whether each statement is true or false. Then write the converse and tell whether it is true or false.

If 鈭�A鈮�鈭�B, then m鈭�A=m鈭�B.
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