Q2 State the hypothesis and the con... [FREE SOLUTION]

91影视

Geometry

Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen

$Math Studyset 91影视 Explanations$ Math

Student Edition 路 227 pages

ISBN: 9780395977279

Chapter 2: Q2 (page 35)

State the hypothesis and the conclusion of each conditional.
I can鈥檛 sleep if I鈥檓 not tired.

Short Answer

Expert verified

The hypothesis is I鈥檓 not tired and the conclusion is I can鈥檛 sleep.

Step by step solution

Step 1. Hypothesis and the conclusion.

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

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.

Step 3. Rewrite the statement.

The given statement 鈥淚 can鈥檛 sleep if I鈥檓 not tired鈥� can be rewritten as 鈥淚f I鈥檓 not tired, then I can鈥檛 sleep鈥�.

Step 4. Identification of Hypothesis and the conclusion.

In the statement 鈥淚f I鈥檓 not tired, then I can鈥檛 sleep鈥�, therefore, 鈥淚鈥檓 not tired鈥� is followed by 鈥淚f鈥� and 鈥淚 can鈥檛 sleep鈥� is followed by 鈥渢hen鈥� thus, the hypothesis is I鈥檓 not tired and the conclusion is I can鈥檛 sleep.

Hence, the hypothesis is I鈥檓 not tired and the conclusion is I can鈥檛 sleep.