Question
In each of the following, determine whether the statement is true or false. If it is true, prove it. If it is false, give an example.
(i) If and , then
(ii) If and , then
(iii) If and , then
(iv) If and , then
(v) If and , then
(vi) If and , then
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Text solutionVerified
(i) False
Let and
and
Now,
However,
(ii) False.
As ,
Let , and
However,
(iii) True
Let and .
Let
(iv) False
As, and
Let , and
However,
(v) False
Let and
Now, and
However,
(vi) True
Let and .
To show:
If possible, suppose .
Then, , which is a contradiction as
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Question Text | In each of the following, determine whether the statement is true or false. If it is true, prove it. If it is false, give an example. (i) If and , then (ii) If and , then (iii) If and , then (iv) If and , then (v) If and , then (vi) If and , then |
Answer Type | Text solution:1 |
Upvotes | 150 |