Chapter 6: Q5. (page 206)

When some people are given that $j > k$ and $l > m$ , they carelessly concluded that $j + k > l + m$ . Find the values for j, k, l, and m that shows this conclusion is false.

Short Answer

Expert verified

The conclusion is false when $j = 3$ , $k = 2$ , $l = 6$ , $m = 5$ and $m = 5$ .

Step by step solution

Step 1. Choose values for j, k, l and m

The values for j, k, l, m can be chosen as $j = 3$ , $k = 2$ , $l = 6$ , $m = 5$

Step 2. Verify the given inequality for j, k, l and m

Since $j = 3$ , $k = 2$ , $l = 6$ , $m = 5$ and $3 > 2$ , $6 > 5$ therefore, $j > k$ and $l > m$ .

Step 3. Check the conclusion

If $j = 3$ , $k = 2$ then $j + k = 3 + 2$ and hence $j + k = 5$ .

Also, if $l = 6$ , $m = 5$ then $l + m = 6 + 5$ and hence $l + m = 11$ .

Since $11 > 5$ therefore $l + m > j + k$ . Contradiction occurs.

Therefore, the conclusion is false.

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When some people are given that $j > k$ and $l > m$ , they carelessly concluded that $j + k > l + m$ . Find the values for j, k, l, and m that shows this conclusion is false.

Short Answer

Step by step solution

Step 1. Choose values for j, k, l and m

Step 2. Verify the given inequality for j, k, l and m

Step 3. Check the conclusion

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When some people are given that j>kand l>m, they carelessly concluded that j+k>l+m. Find the values for j, k, l, and m that shows this conclusion is false.

Short Answer

Step by step solution

Step 1. Choose values for j, k, l and m

Step 2. Verify the given inequality for j, k, l and m

Step 3. Check the conclusion

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Logic and Functions

Discrete Mathematics

Geometry

Theoretical and Mathematical Physics

Calculus

Study anywhere. Anytime. Across all devices.

When some people are given that $j > k$ and $l > m$ , they carelessly concluded that $j + k > l + m$ . Find the values for j, k, l, and m that shows this conclusion is false.