Q10. For each statement in Ex 5-10 co... [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 6: Q10. (page 211)

For each statement in Ex 5-10 copy and complete a table like the one shown below.
If $x^{2} > 1$ , then $x > 1$ .

Short Answer

Expert verified

Statement	If $\underset{炉}{?}$ , then $\underset{炉}{?}$	True/false
1. Given	If $x^{2} > 1$ , then $x > 1$	False
2. Contrapositive	If not $x > 1$ , then not $x^{2} > 1$	False
3. Converse	If $x > 1$ then $x^{2} > 1$	True
4. Inverse	If not $x^{2} > 1$ then not $x > 1$	True

Step by step solution

Step 1. Define contrapositive, inverse, and converse for the given statement

If the given statement is 鈥樷€橧f p then q鈥欌€�, the contrapositive is 鈥樷€橧f not q then not p鈥欌赌�.

If the given statement is 鈥樷€橧f p then q鈥欌€�, the inverse is 鈥樷€橧f q then p鈥欌赌�.

If the given statement is 鈥樷€橧f p then q鈥欌€�, the converse is 鈥樷€橧f not p then not q鈥欌赌�.

Step 2. Contrapositive of the given statement

The given statement is If $x^{2} > 1$ , then $x > 1$ is false.

The contrapositive of the given statement is If not $x > 1$ , then not $x^{2} > 1$

Thus, it is false.

Step 3. Check inverse and converse of the given statement

The converse of the given statement is If $x > 1$ then $x^{2} > 1$

Thus, it is true.

The inverse of the given statement is If not $x^{2} > 1$ then not $x > 1$ .

Thus, it is true.

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91影视

For each statement in Ex 5-10 copy and complete a table like the one shown below.
If $x^{2} > 1$ , then $x > 1$ .

Short Answer

Step by step solution

Step 1. Define contrapositive, inverse, and converse for the given statement

Step 2. Contrapositive of the given statement

Step 3. Check inverse and converse of the given statement

One App. One Place for Learning.

Most popular questions from this chapter

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91影视

For each statement in Ex 5-10 copy and complete a table like the one shown below.If x2>1, then x>1.

Short Answer

Step by step solution

Step 1. Define contrapositive, inverse, and converse for the given statement

Step 2. Contrapositive of the given statement

Step 3. Check inverse and converse of the given statement

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Decision Maths

Theoretical and Mathematical Physics

Pure Maths

Mechanics Maths

Geometry

Study anywhere. Anytime. Across all devices.

For each statement in Ex 5-10 copy and complete a table like the one shown below.
If $x^{2} > 1$ , then $x > 1$ .