Induction & Deduction_#PSC_TSC

 

Induction & Deduction

Directions: In each question below are given two statements followed by two conclusions numbered I and II. Yu have to take the given two statements to be true even if they seem to be at variance from commonly known facts. Read the conclusion and then decide which of the given conclusions logically follows from the two given statements, disregarding commonly known facts. 

Give answer

(a) if only conclusion I follows;

(b) if only conclusion II follows;

(c) if either conclusion I or II follows;

(d) if neither conclusion I nor II follows;

(e) if both conclusions I and II follow.

1.       Statements : All men are dogs. All dog are cats.  

          Conclusions :                                                     I. All men are cats      II. All cats are men

2.       Statements : All film stars are playback singers. All film directors are film stars.

          Conclusions :                                                     I. All film directors are playback signers.

                            : Some film stars are film directors.

3.       Statements : All pens are roads. All roads are houses.

          Conclusions :                                                     I. All houses are pens.            II. Some houses are pens.

Directions: In each of the following questions, two statements are given followed by three or conclusions numbered I, II, III and IV. You have to take the given two take the given statements to be true even if they seem to be at variance from commonly known facts and then decide which of the given conclusions logically follows from the given statements, disregarding commonly known facts. 

4.       Statements : All aeroplanes are trains. Some trains are chairs.

          Conclusions :    I.                                               Some aeroplanes are chairs.   II.        Some chairs are aeroplanes.

                               III.                                                 Some chairs are trains            IV.       Some trains are aeroplanes

          (a)   None follows                                                      (b)           Only I and II follow

          (c)   Only II and III follow                                 (d)   Only III and IV follow

5.       Statements : Some bottles are drinks. All drinks are cups.

          Conclusions :    I.                                               Some bottles are cups.           II.        Some cups are drinks

                               III.                                                 All drinks are bottles.             IV.       All cups are drinks.

          (a)   Only I and II follow                                    (b)   Only II and III follow

          (c)   Only II and IV follow                                 (d)   Only III and IV follow

          (e)   Only I and IV follow

6.       Statements : Some books are pens. No pen is pencil.

          Conclusions :    I.                                               Some pens are books.             II.        Some pencil are books.

                               III.                                                 Some books are not pencils.   IV.       All pencils are books.

          (a)   Only I follows                                             (b)   Only II and III follow

          (c)   Only I and III follow                                  (d)   Only I and II follow      

 

7.       Statements : Some clothes are marbles. Some marbles are bags.

          Conclusions :    I.                                               No cloth is a bag.       II.        All marbles are bags.

                               III.                                                 Some bag are clothes. IV.       No marble is a cloth.

          (a)   Only either I or IV follows                         (b)   Only either I or II follows

          (c)   None follows                                               (d)   Only either I or III follows

Answer With Explanation

1.  (a) Since both the premises are universal and affirmative, the conclusion must be universal affirmative. However, conclusion II, being an A-type proposition, distributes the term 'goats'. Since the term 'goats' is distributed in II without being distributed in any of the premises, so conclusion II cannot follow. Thus, only I follows.

2.  (e) Since both the premises are universal and affirmative, the conclusion must be universal affirmative and should not contain the middle term. So, I follows. I is the converse of the second premise and so it also holds.

3.  (b) Since both the premises are universal and affirmative, the conclusion must be universal affirmative and should not contain the middle term. So, it follows that 'All pens are houses'. II is the converse of this conclusion and so it holds. Since the term 'houses' is distributed in I without being distributed in any of the premises, so I does not follow.

4.  (d)       Since the middle term 'train's is not distributed even once in the premises, no definite conclusion follows. However, III is the converse of the second premise while IV is the converse of the first premise. So, both of them hold.   

5.  (a) Since one premise is particular, the conclusion must be particular and should not contain the middle term. So, it follows that 'Some bottles are cups'. Thus I follows. It is the converse of the second premise and so it also holds.

6.  (c) Since one premise is particular and the other negative, the conclusion must be particular negative and should not contain the middle term. Thus, III follows. I is the converse of the first premise and so it also holds.

7.  (d)       Since both the premises are particular, no definite conclusion follows. However, I and III involve only the extreme terms and form a complementary pair. Thus, either I or III follows.

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