5. Considering given statements as true, select a logical conclusion based on the given statements.
Statements:
Some roads are highways.
Some highways are seaways.
Some seaways are airways.
Conclusions:
I. Some airways are roads.
II. Some seaways are roads.
III. Some airways are highways.
IV. Some roads are airways.
a. Only III and IV follow
b. Only III and IV follow
c. Only I and II follow
d. All of conclusions follow
e. None of the above follow
Answer: e. None of the above follow
Explanation:
For a conclusion to be true, it has to be true in every possible Venn diagram.
From given Venn diagram, we can say that none of the above conclusions always follows.
6. Considering given statements as true, select a logical conclusion based on the given statements.
Statements:
All boots are sandals.
No sandal is shoe.
All shoes are rings.
Conclusions:
I. Some boots are rings.
II. All sandals are boots.
III. Some rings are sandals.
IV. All rings are shoes.
a. Either I or II follow
b. Either III or IV follow
c. Only II and IV follow
d. Neither I nor II follow
e. All of the above follow
Answer: d. Neither I nor II follow
Explanation:
For a conclusion to be true, it has to be true in every possible Venn diagram. Here one of the possible diagram is given, in which, no conclusion follows. So only correct option is d.
7. Considering given statements as true, select a logical conclusion based on the given statements.
Statements:
Some Q are E.
All E are D.
No D is A.
Conclusions:
I. Some Q are not A.
II. Some Q are not D.
III. All Q are D.
IV. No Q is A.
a. Only III follows
b. Either I or IV follow
c. Either II or III follow and I follows
d. Only IV follows
e. All of the above follow
Answer: c. Either II or III follow and I follows
Explanation:
For a conclusion to be true, it has to be true in every possible Venn diagram.
From given Venn diagrams, we can say that conclusion I always follows.
Also, drawing all possible Venn diagrams show that satisfying conditions in given statements, either conclusion II or III will be true. Both cannot be true simultaneously. It is either one of the two.
8. Considering given statements as true, select a logical conclusion based on the given statements.
Statements:
All mangoes are fruits.
No fruit is an apple.
Some apples are vegetables.
Some fruits are carrots.
Conclusions:
I. No mango is an apple.
II. Some vegetables are not apples.
III. Some mangoes are carrots.
IV. Some vegetables are apples.
a. Only I and IV follow
b. Only I, II or IV follows
c. Either III or IV follow and I follows
d. Either II or IV follows
e. None of the above options.
Answer: a. Only I and IV follow
Explanation:
For a conclusion to be true, it has to be true in every possible Venn diagram. II and III are not true for following Venn diagram.
