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Which of the following formulas represents the sentence, 'Share prices will go up, and if interest rates go up too, there will be a recession', where ;

p means 'share prices will go up'

q means 'interest rates will go up'

r means 'there will be a recession'.

(A)p∧q→r

(B)p∧(q→r)

(C)p→q∧r

(D)(p→q)∨r

I am confused to choose between A and B, because of "too".

Please help.

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I'd say B, as the statement implies that share prices will definitely go up, and A is not saying that.

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  • $\begingroup$ @Bram-Thanks.Got it. :) $\endgroup$ – user3767495 Dec 11 '18 at 4:45
  • $\begingroup$ @user3767495 You're welcome! :) $\endgroup$ – Bram28 Dec 11 '18 at 13:26
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It is not D since if share prices go up this doen't mean that the intrest rates will go up.

It is not C since it is saying that (if p) then (...) and p doesn't need an 'if' in this case because it is always true, it can't be false (i.e. share prices will go up and there is no chance that they won't).

And similarly it is not A, since it start with (if p and q are both true) then (...), which means that A gives a chance that [(p is false) or (q is false)] which migh imply that (p is false) but as we just said for part C, p is always true and it can't be false.

So I also see that part B is the right answer, and we can understand its statement as (p is true) and (if q is true then r is true) i.e. (share prices will go up) and (if interest rates will go up then there will be a reccession)

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