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verify this (functions)

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Arushi :))

verify this (functions)

consider the following statements
1) there exists an element x in the domain of f such that no element in the codomain is associated with it.
2) there exists an element x in the domain of f & two distinct elements z & w in the codomain of f such that both z & w are associated with x.
Q1) Which of the foll is true?
a. to prove f is not a function it is necessary to demonstrate statement1
b.to prove f is not a function it is necessary to demonstrate statement2
c.to prove f is not a function it is necessary to demonstrate statement1 or 2
d. none of the abve
Q2) which of the following is true?
a. demonstration of 1 is sufficient to prove f is not a function but demonstration of 2 is not sufficient to prove that f is not a function.
b.demonstration of 2 is sufficient to prove f is not a function but demonstration of 1 is not sufficient to prove that f is not a function.
c. demonstration of 1 & 2 is sufficient to prove f is not a function.
d. none of the above
ANSWER for ques 1 is c
n for ques 2 it is d. please verify

vandita24x7

Re: verify this (functions)

I agree with you on both the answers

On Sat, Feb 22, 2014 at 6:54 PM, Arushi :) [via Discussion forum] <[hidden email]> wrote:

consider the following statements
1) there exists an element x in the domain of f such that no element in the codomain is associated with it.
2) there exists an element x in the domain of f & two distinct elements z & w in the codomain of f such that both z & w are associated with x.
Q1) Which of the foll is true?
a. to prove f is not a function it is necessary to demonstrate statement1
b.to prove f is not a function it is necessary to demonstrate statement2
c.to prove f is not a function it is necessary to demonstrate statement1 or 2
d. none of the abve
Q2) which of the following is true?
a. demonstration of 1 is sufficient to prove f is not a function but demonstration of 2 is not sufficient to prove that f is not a function.
b.demonstration of 2 is sufficient to prove f is not a function but demonstration of 1 is not sufficient to prove that f is not a function.
c. demonstration of 1 & 2 is sufficient to prove f is not a function.
d. none of the above
ANSWER for ques 1 is c
n for ques 2 it is d. please verify

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Amit Goyal

Re: verify this (functions)

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In reply to this post by Arushi :))

For Question (1), answer is (c) to prove f is not a function it is necessary to demonstrate statement 1 or 2.
For Question (2), answer is (c) demonstration of 1 & 2 is sufficient to prove f is not a function.

vandita24x7

Re: verify this (functions)

For the second Question Shouldn't the right answer be "demonstration of 1 "or" 2 is sufficient to show f is not a function... ??? Thats y i chose to go with option d. Please Explain

On Sat, Feb 22, 2014 at 8:31 PM, Amit Goyal [via Discussion forum] <[hidden email]> wrote:

For Question (1), answer is(c) to prove f is not a function it is necessary to demonstrate statement 1 or 2.For Question (2), answer is(c) demonstration of 1

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Arushi :))

Re: verify this (functions)

yes, even i thought so.. Its given ''and''

vandita24x7

Re: verify this (functions)

Arushi , u r preparing for M.A Eco?

On Sat, Feb 22, 2014 at 9:27 PM, Arushi :) [via Discussion forum] <[hidden email]> wrote:

yes, even i thought so.. Its given ''and''

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vandita24x7

Re: verify this (functions)

In reply to this post by Arushi :))

Amit Goyal Please respond............

On Sat, Feb 22, 2014 at 9:30 PM, vandita mishra <[hidden email]> wrote:

Arushi , u r preparing for M.A Eco?

On Sat, Feb 22, 2014 at 9:27 PM, Arushi :) [via Discussion forum] <[hidden email]> wrote:

yes, even i thought so.. Its given ''and''

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Arushi :))

Re: verify this (functions)

ya.. obviously. thats what brings me here

Amit Goyal

Re: verify this (functions)

Administrator

In reply to this post by vandita24x7

Here is the reason why:

Given: (A is true or B is true) implies C is true. That is, (A is true or B is true) is sufficient for C is true.
To prove: (A is true and B is true) implies C is true. That is, (A is true and B is true) is sufficient for C is true.

Proof:
Clearly, (A is true and B is true) implies (A is true or B is true). Since, (A is true or B is true) implies C is true. Hence, (A is true and B is true) implies C is true. Thus, (A is true and B is true) is sufficient for C is true.

vandita24x7

Re: verify this (functions)

I still don't get you. Can you use mathematical symbols where required.. as i m getting confused with the words "or" and "and" as to what means what in diff places. Please

On Sat, Feb 22, 2014 at 10:05 PM, Amit Goyal [via Discussion forum] <[hidden email]> wrote:

Here is the reason why:

Given: (A it true or B is true) implies C is true. That is, (A it true or B is true) is sufficient for C is true.
To prove: (A it true and B is true) implies C is true. That is, (A it true and B is true) is sufficient for C is true.

Proof:
Clearly, (A it true and B is true) implies (A it true or B is true). Since, (A it true or B is true) implies C is true. Hence, (A it true and B is true) implies C is true. Thus, (A it true and B is true) is sufficient for C is true.

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vandita24x7

Re: verify this (functions)

In reply to this post by Amit Goyal

why (A it true and B is true) implies (A it true or B is true) ??

On Sat, Feb 22, 2014 at 10:13 PM, vandita mishra <[hidden email]> wrote:

I still don't get you. Can you use mathematical symbols where required.. as i m getting confused with the words "or" and "and" as to what means what in diff places. Please

On Sat, Feb 22, 2014 at 10:05 PM, Amit Goyal [via Discussion forum] <[hidden email]> wrote:

Here is the reason why:

Given: (A it true or B is true) implies C is true. That is, (A it true or B is true) is sufficient for C is true.
To prove: (A it true and B is true) implies C is true. That is, (A it true and B is true) is sufficient for C is true.

Proof:
Clearly, (A it true and B is true) implies (A it true or B is true). Since, (A it true or B is true) implies C is true. Hence, (A it true and B is true) implies C is true. Thus, (A it true and B is true) is sufficient for C is true.

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Amit Goyal

Re: verify this (functions)

Administrator

In reply to this post by vandita24x7

Solution is mathematical symbols is attached.
Sol.png

vandita24x7

Re: verify this (functions)

Why does (A intersection B) imply (A union B) ??

On Sat, Feb 22, 2014 at 10:41 PM, Amit Goyal [via Discussion forum] <[hidden email]> wrote:

Solution is mathematical symbols is attached.
Sol.png

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vandita24x7

Re: verify this (functions)

In reply to this post by Amit Goyal

Okk got it

vandita

On 22 Feb 2014 22:13, "vandita mishra" <[hidden email]> wrote:

I still don't get you. Can you use mathematical symbols where required.. as i m getting confused with the words "or" and "and" as to what means what in diff places. Please

On Sat, Feb 22, 2014 at 10:05 PM, Amit Goyal [via Discussion forum] <[hidden email]> wrote:

Here is the reason why:

Given: (A it true or B is true) implies C is true. That is, (A it true or B is true) is sufficient for C is true.
To prove: (A it true and B is true) implies C is true. That is, (A it true and B is true) is sufficient for C is true.

Proof:
Clearly, (A it true and B is true) implies (A it true or B is true). Since, (A it true or B is true) implies C is true. Hence, (A it true and B is true) implies C is true. Thus, (A it true and B is true) is sufficient for C is true.

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