Q7 Rewrite each pair of conditional... [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: Q7 (page 35)

Rewrite each pair of conditionals as a biconditional.
If B is between A and C, then .
If , then B is between A and C.

Short Answer

Expert verified

The biconditional of both the statements is-

鈥�B is between A and C if and only if 鈥�.

鈥� if and only if B is between A and C鈥�.

Step by step solution

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�.

Step 2. Rewrite statement 1 as biconditional.

The given statement 鈥淚f B is between A and C, then .鈥� has hypothesis p as B is between A and C conclusion as , therefore, biconditional will be 鈥�B is between A and C if and only if 鈥�.

Step 3. Rewrite statement 2 as biconditional.

The given statement 鈥淚f , then B is between A and C.鈥� has hypothesis p as and conclusion q as B is between A and C, therefore, biconditional will be 鈥� if and only if B is between A and C鈥�.