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Chapter 2: Q24 (page 35)

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

x=1only if x2=x.

Short Answer

Expert verified

The statement "x=1 only if x2=x", " is true.

The converse of the given statement 鈥淚fx2=x then x=1.鈥� is false.

Step by step solution

01

Step 1. Converse of a conditional.

The converse of the conditional is obtained by interchanging the hypothesis and the conclusion. If p represents the hypothesis and q represents the conclusion, then converse of the statement 鈥淚f p, then q鈥� will be 鈥淚f q, then p鈥�.

02

Step 2. State whether the statement is true or not.

The statement "x=1only if x2=x", Here, the given statement is of the form p only if q.

Here p is x=1and q is x2=x.

If x=1,

12=1

1=1True

Therefore, the statement is true.

03

Step 3. Write the converse.

The converse is of the form "if q, then p 鈥�

Therefore, the converse of the given statement is 鈥� 鈥淚f x2=xthen x=1.鈥�

04

Step 4. State whether the converse is true or not.

In order to verify if the converse is true or not let solve x2=x.

x2=xx2鈭�x=0xx鈭�1=0x=0,1

That is x may be 0 also.

Therefore, the converse of the given statement is false.

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Most popular questions from this chapter

Give an example of a false conditional whose converse is true.

Justify each statement with a property from algebra or property of congruence 鈭�P鈮�鈭�P.

Copy everything shown and supply missing statements and reasons.

Given:

m鈭�1=m鈭�3;

m鈭�2=m鈭�4

Prove: m鈭�ABC=m鈭�DEF

Proof:

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

If EB鈫� is the bisector of 鈭�AEC, then m鈭�AEB=12m鈭�AEC .

If 鈭�Aand 鈭�Bare supplementary, find the value of x, m鈭�Aand m鈭�B.

25. role="math" m鈭�A=x+16,m鈭�B=2x-16
See all solutions

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