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Among the following, there are two statements which can't be true together, but can be false together. Select the code that represents them. a) All poets are dreamers. b) No poets are dreamers. c) Some poets are dreamers. d) Some poets are not dreamers.

Among the following, there are two statements which can't be true together, but can be false together. Select the code that represents them. a) All poets are dreamers. b) No poets are dreamers. c) Some poets are dreamers. d) Some poets are not dreamers. Correct Answer a and b

An option is correct only if both of the following conditions are satisfied:

1) Both the statements cannot be true at a time

2) Both the statements can be false at a time

Let's use the process of elimination to find the correct answer.

Option 2: a and d

a is true ⇒ there is no poet who is not a dreamer. Therefore, d will be false.

Therefore, both a and d cannot be true together.

a is false ⇒ there exists at least one poet who is not a dreamer. Thus, d will be true.

Therefore, both a and d cannot be false together.

Hence, option 2 is dismissed.

Option 3: b and d

b is true ⇒ there is at least one poet who is not a dreamer. Thus, d will become true.

Therefore, we have both b and d can be true together.

Hence, option 3 is ruled out.

Option 4: c and d

c is true ⇒ there is at least one poet who is a dreamer. Now, some of the remaining poets may or may not be dreamers.

Thus, d can be true when c is true.

Therefore, we have both c and d can be true together.

Hence, option 4 is also eliminated.

Option 1: a and b

a is true ⇒ every poet is a dreamer. Therefore, b cannot be true.

Thus, both a and b cannot be true together.

Now, a is false if there is at least one poet who is not a dreamer and b is false if there is at least one other poet who is a dreamer.

Thus, it is possible for a and b to be false at a time.

Hence, option 1 is the correct answer.

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