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Given below are two premises (a) and (b). Four conclusions are drawn from them. Select the code that states validly drawn conclusion(s) [taking the premises individually or jointly] Premises : (a) Some women are teachers. (b) All teachers are hard-working. Conclusions: (i) All hard-working people are teachers. (ii) All teachers are not women. (iii) Some hard-working teachers are women. (iv) Some women are hard-working

Given below are two premises (a) and (b). Four conclusions are drawn from them. Select the code that states validly drawn conclusion(s) [taking the premises individually or jointly] Premises : (a) Some women are teachers. (b) All teachers are hard-working. Conclusions: (i) All hard-working people are teachers. (ii) All teachers are not women. (iii) Some hard-working teachers are women. (iv) Some women are hard-working Correct Answer (iii) and (iv)

The least possible Venn diagram for the given statements is as follows,

[ alt="antesh29" src="//storage.googleapis.com/tb-img/production/20/09/antesh29.PNG" style="width: 307px; height: 100px;">

(i) All hard-working people are teachers → False (It is possible but not definite)

(ii) All teachers are not women → False (It is possible but not definite)

(iii) Some hard-working teachers are women → True (Some teachers who is hardworking is also women)

(iv) Some women are hard-working → True (Some women who is  teacher is also hard-working)

Hence, (iii) and (iv) is the correct answer.

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