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# Given that all A's are B's, which of the following

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Manager
Status: faciendo quod indiget fieri
Joined: 13 Mar 2012
Posts: 85
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Kudos [?]: 38 [0], given: 4

Given that all A's are B's, which of the following [#permalink]

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05 Sep 2012, 04:10
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Given that all A's are B's, which of the following inferences can be drawn?

1) No A is not a B
2) All B's are A's
3) Some B's are not A's

thanks

[Reveal] Spoiler:
I want to know why isnt 3 an inference.? Answer is only 1
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Senior Manager
Joined: 28 Jun 2009
Posts: 445
Location: United States (MA)
Followers: 18

Kudos [?]: 176 [0], given: 46

Re: draw an inference [#permalink]

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05 Sep 2012, 15:21
I want to know why isnt 3 an inference.? Answer is only 1

Given : all A's are B's

So lets say, A's are apples and B's are fruits.

1. No A is not a B >> No apple is not fruit >> all apples are fruits >> satisfies
2. All B's are A's >> All fruits are apples >> certainly not true
3. Some B's are not A's >> Some fruits are not apples >> satisfies

Lets take another example, since we have alreday ruled out ans choice 2, we will not validate it with different example.

A = apple B = apple

1. No A is not a B >> No apple is not apple >> all apples are apples >> satisfies
3. Some B's are not A's >> Some apples are not apples >> not true

So 1 stands valid in all cases.

You can do the same using sets.

A = {1,2,3} and B = {1,2,3} OR B = {1,2,3,4}
Re: draw an inference   [#permalink] 05 Sep 2012, 15:21
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# Given that all A's are B's, which of the following

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