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Chapter 6: Q14. (page 211)

What can you conclude by using the given statement together with each additional statement? If no conclusion is possible, say so.

Given: All my students love geometry.

a. Stu is my student.

b. Luis loves geometry.

c. Stella is not my student.

d. George does not love geometry.

Short Answer

Expert verified

a. Theconclusion is 鈥淪tu loves geometry鈥�.

b.There is no conclusion.

c.There is no conclusion.

d.The conclusion is 鈥淕eorge is not my student鈥�.

Step by step solution

01

a.Step 1 – Define the additional given statement.

The given statement is 鈥渁ll my students love geometry鈥�

The given additional statement is 鈥淪tu is my student鈥�. If she/he is my student then it means that he/she loves geometry.

02

– Explanation

Stu is my student, so, he loves geometry.

03

– Conclusion for given statement together additional statement

Hence, the conclusion is 鈥淪tu loves geometry鈥�.

04

b.Step 1 – Define the additional given statement

The given statement is 鈥渁ll my students love geometry鈥�.

The given additional statement is 鈥淟uis loves geometry鈥�. By the given statement there is no clue that Luis is my student or not.

05

– Explanation

Luis loves geometry, but we don鈥檛 know he is my student or not.

06

– Conclusion for given statement together additional statement

Hence, no conclusion is possible.

07

c.Step 1 – Define the additional given statement

The given statement is 鈥渁ll my students love geometry鈥�.

The given additional statement is 鈥淪tella is not my student鈥�. It means that Stella may or may not loves geometry.

08

– Explanation

Stella is not my student, but she may or may not loves geometry.

09

– Conclusion for given statement together additional statement

Hence, there is no conclusion possible.

10

d.Step 1 – Define the additional given statement

The given statement is 鈥渁ll my students love geometry鈥�

The given additional statement is 鈥淕eorge does not love geometry鈥�

11

– Explanation

George does not love geometry, so he is not my student.

12

– Conclusion for given statement together additional statement

Hence, the conclusion is 鈥淕eorge is not my student鈥�.

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