Some radios are telephones + All telephones are mirrors = I + A = I = Some radios are mirrors Hence II follows Some radios are mirrors + All mirrors are desks = I + A = I = Some radios are desks Hence I follows. All telephones are mirrors + All mirrors are desks = A + A + = All telephones are desks ? conversion ? Some desks are telephones (I). Hence III follows.
Both the Premises are Universal Affirmative (A?type).
All elephants are men. ? All men are socks.
A + A ? A?type of Conclusion "All elephants are socks."
This is Conclusion II.
Conclusion I is the Converse of it.
Both the Premises are Universal Affirmative (A ? type).
Rajiv is a boy. ? All boys are tall.
A + A ? A-type of Conclusion "Rajiv is tall".
This is Conclusion I.
Venn diagrams:
All the three Premises are particular (I?type). No Conclusion follows from the two particular premises.
First Premise is Universal Affirmative (A-type).
Second Premise is Particular Affirmative (I-type).
Some men are stenographers. ? All stenographers are lazy.
I + A ? I-type of Conclusion "Some men are lazy".
This is Conclusion II.
Mary always tells the truth. Therefore, both Mary and Ann have cats. Clearly, Ann is lying. Thus, all the Conclusions I, II and III follow.
All furniture are jungles + No jungle is road = A + E = E = No furniture is road ? conversion ? No road is furniture (E) Hence I does not follows. All furniture are jungles (A) ? conversion ? Some jungles are furniture (I). Hence II follows. No jungle is road + Some roads are hills = E + I = O* = Some hills are not jungles Hence III does not follows.
Some stones are rocks + All rocks are mountains = I + A = I = Some stones are mountains ? conversion ? Some mountains are stones (I). Hence II follows. All brick are stones + Some stones are mountains = A + I = No conclusion Hence II does not follow. All brick are stones (A) ? conversion ? Some stone are bricks(I). Hence III follows.
Some pates are chairs + All chairs are tables = I + A = I = Some plates are tables ? conversion ? Some tables are plates(I). Hence I follows. Some bags are plates + Some plates are chairs = I + I = No conclusion Hence II and III do not follow. By combination. However, the two form a complementary E-I pair, Hence either I or III follows.
Some rooms are halls + All halls are leaves = I + A = I = Some rooms are leaves ? conversion ? Some leaves are rooms(I) Hence III follows. All desks are rooms + Some rooms are halls = A + I = No conclusion Hence II and consequently I do not follow.
All teachers are lawyers (A) ? conversion ? Some lawyers are teachers (I). Hence IV follows. Now, Some doctors are lawyers + Some lawyers are teachers = I + I = No conclusion Hence I does not follow. Some engineers are lawyers (I) ? conversion ? Some lawyers are engineers + All engineers are businessmen = I + A = I = Some lawyers are businessmen ? conversion Some businessmen are lawyers Hence II follows. But , All teachers are lawyers + Some lawyers are businessmen = A + I = No conclusion Hence III does not follow.
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