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Chapter 2: Q5 (page 34)

State the hypothesis and the conclusion of each conditional.

if

Short Answer

Expert verified

The hypothesis is and the conclusion is .

Step by step solution

01

Step 1. Hypothesis and the conclusion.

The hypothesis and the conclusion of a conditional statement are where the hypothesis is the phrase immediately following by the word if and the conclusion is the phrase immediately following by the word then.

02

Step 2. Symbolic representation.

If p represents the hypothesis and q represents the conclusion, then the basic form of an if-then statement is 鈥淚f p, then q鈥�. For example, in the statement 鈥淚f today is Friday, then tomorrow is Saturday鈥�, 鈥渢oday is Friday鈥� is the Hypothesis, and 鈥渢omorrow is Saturday鈥� is the Conclusion.

03

Step 3. Rewrite the statement.

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

04

Step 4. Identification of Hypothesis and the conclusion.

Since, 鈥�鈥� is followed by 鈥淚f鈥� and 鈥�鈥� is followed by then 鈥渢hen鈥� thus, the hypothesis is and the conclusion is .

Hence, the hypothesis is and the conclusion is .

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Most popular questions from this chapter

Prove the following statement by filling in the blanks.

If A and B have coordinated a and b, with b>a, and the midpoint M of AB炉 has coordinate x, then prove x=a+b2.

Proof:

Statement

Reasons

1. A, M, and B have coordinated a, x, and b respectively; b>a.

1. ?

2. AM=x鈭�a;MB=b鈭�x

2. ?

3. M is the midpoint of AB炉.

3. ?

4. AM炉鈮�MB炉, orAM=MB

4. ?

5.x鈭�a=b鈭�x

5. ?

6. 2x=?

6. ?

7. x=a+b2

7. ?

Provide a counterexample to show that each statement is false.

Statement: If a four-sided figure has four congruent sides, then it has four right angles.

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.

P is the midpoint ofGH炉 implies that GH=2PG.

Provide a counterexample to show that each statement is false. You may use words or draw a diagram.

If a number is divisible by 4, then it is divisible by 6.
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