Reasoning: Syllogism Questions Set 18

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Direction (1-6): Each option contains some statements. Determine from which statements the given two conclusions follow.

  1. Conclusions:
    I. All tigers are dogs is a possibility
    II. Some lions are cats.
    Statements:
    A) All dogs are lions. Some cats are dogs. No lion is tiger.
    B) Some dogs are lions. Some tigers are lions. No cat is tiger.
    C) Some dogs are lions. All cats are lions. No cat is tiger.
    D) All dogs are lions. All tigers are lions. No cat is tiger.
    E) None of these
    View Answer
    Option C
    Solution:
    In C) Reverse the statement: All tigers are lions. => Some lions are tigers
    All dogs are lions + Some Lions are tiger = All+ Some=> no conclusion between Dogs and tigers but any possibility between Dogs and tiger will be true. So I follows
    For II. Some cats are tigers. All tigers are lions. => Some + All= Some => Some cats are lions => Some lions are cats. So II. is true
  2. Conclusions:
    I. Some scales are pen. 
    II. Some pencils are not erasers.
    Statements:
    A) Some pens are pencils. All pencils are scales. All scale is eraser.
    B) Some pens are pencils. All pencils are scales. No pen is eraser.
    C) All pens are pencils. No pencil is scale. Some scales are erasers.
    D) Some pens are pencils. All scales are pencils. Some scales are erasers.
    E) None is correct
    View Answer
      Option B
    Solution:
    In B) For I.  Some pens are pencils. All pencils are scales=> Some + All= Some=> Some pens are scales = Some scales are pen. So I is true
    For II. Some pencils are pens + No Pen is eraser=> Some + No= Some Not= Some pencils are not eraser.
  3. Conclusions:
    I. No blue is white
    II. All white are green is a possibility.
    Statements:
    A) Some green are blue. No blue is red. Some white are red.
    B) All green are blue. No blue is red. All white are red.
    C) All green are blue. Some blue are red. All white are red.
    D) Some green are blue. No blue is red. All white are red.
    E) None is correct
    View Answer
    Option D
    Solution:

    In D) For I. All white is red+ No red is blue=> All + No= No=> No white is blue=> No blue is white
    For II. All white are red+ No red is blue + Some blue are green => (All + No) + Some = No + Some= Some not reversed => Some green are not white. => All white being green is a possibility [When Some A are not B => All B being A is a possibility is true]
  4. Conclusions:
    I. Some blue are red is a possibility.
    II. Some green are not red.
    Statements:
    A) Some green are white. All white are blue. No white is red.
    B) All green are white. No white is blue. Some blue are red.
    C) Some green are white. Some white are blue. All blue are red.
    D) All green are white. No white is red. All blue are red.
    E) None is correct
    View Answer
      Option A
    Solution:
    In A) For I. No red is white+ All white is blue => Some not reversed=> Some blue are not red => Some blue are red is a possibility is true
    For II. Some green are white. No white is red. =>Some + No = Some Not = Some green are not red
  5. Conclusions:
    I. All dollar are rupee is a possibility.
    II. Some pound are not dollar.
    Statements:
    A) No dollar is yen. All rupee are yen. Some yen are pound.
    B) No dollar is yen. Some yen are rupee. Some rupee are pound.
    C) No dollar is yen. All yen are rupee. Some yen are pound.
    D) All dollar is yen. No yen is rupee. Some rupee are pound.
    E) None is correct
    View Answer
      Option C
    Solution:
    In C) For I. No dollar is yen. All yen are rupee.=> No + All= Some not reversed= Some rupee are not dollar. => All dollar being rupee is a possibility
    For II. No dollar is yen. + Some yen are pound. => No + Some= Some not reversed=> Some pound are not dollar
  6. Conclusions:
    I. Some dogs are frogs is a possibility.
    II. All cats are frogs is a possibility.
    Statements:
    A) Some cats are dogs. No monkey is dog. All frogs are monkeys.
    B) All cats are dogs. Some monkeys are cats. No frog is monkey.
    C) Some cats are monkeys. No dog is monkey. All frogs are monkeys.
    D) All cats are dogs. All monkeys are dogs. No frog is monkey.
    E) None is correct
    View Answer
      Option D
    Solution:
    In D) For I. No frog is monkey + All monkeys are dogs => No + All= some not reversed = Some dogs are not frog.=> Some dogs are frogs is a possibility
    For II. No frog is monkey. +  All monkeys are dogs.= No + All = Some not reversed = Some Frog are not dog
    All cats are dogs.  + Some Frog are not dog (Exceptional Case 2) => Some frogs are not Cat=> All cats are frog is a possibility

Directions (7-10): In each of the questions below, statements are given followed by two conclusions numbered I and II. Read all the conclusions and then decide which of the given conclusions follow from the given statements.

  1. Statements: Some dogs are lions. All cats are lions. No cat is tiger. Some tigers are frogs.
    Conclusions:
    I. No lion is tiger.
    II. Some cats are not frogs
    A) only I follows
    B) only II follows
    C) either I or II follows
    D) neither I nor II follow
    E) both I and II follow
    View Answer
     Option D
    Solution:
    For I: Reverse of No cat is tiger = No tiger is cat + All cat is lion= No + All  = Some not reverse= Some lion are not tiger. So I. is false
    II. No cat is tiger. Some tigers are frogs.=> No + All= Some not reversed = Some frogs are not cats. hence II is false
  2. Statements: Some green are blue. No blue is red. All white are red. Some black are red.
    Conclusions:
    I. All blue are black is a possibility.
    II. No blue is white.
    A) only I follows
    B) only II follows
    C) either I or II follows
    D) neither I nor II follow
    E) both I and II follow
    View Answer
     Option E
    Solution: 

    For I. No blue is red. + Some red are black= No + Some= Some not reversed=> Some black are not blue=> All blue being black is a possibility
    For II. All white is red+ No red is blue => All + No = No=> No white is blue= No blue is white
  3. Statements: No dollar is yen. All yen are rupee. Some yen are pound. All pound are euro.
    Conclusions:
    I. All euro are yen is a possibility. 
    II. No dollar is pound.
    A) only I follows
    B) only II follows
    C) either I or II follows
    D) neither I nor II follow
    E) both I and II follow

    View Answer
     Option A
    Solution: 
    For I. Some yen are pound. All pound are euro.=> Some + All= Some => Some yen are euro => All yen are Euro is a possibility is true
    For II. No dollar is yen. Some yen are pound. => No+ Some= Some not reversed=> Some pound are not dollar. So II. is false
  4. Statements: All cats are dogs. All monkeys are dogs. No frog is monkey. All lions are frogs.
    Conclusions:
    I. No dog is lion
    II. All cats are lions is a possibility 
    A) only I follows
    B) only II follows
    C) either I or II follows
    D) neither I nor II follow
    E) both I and II follow

    View Answer
     Option B
    Solution:
    For I: No frog is monkey+ All monkey are dogs=> No+ All= Some not reversed= Some dogs are not frogs
    All lions are frogs. +  Some dogs are not frogs (Exceptional Case 2)=> Some dogs are not lion. So II. is false
    For II. To get a relation between Cats and Lions: We have to utilize all four statements: Of these four, three start with ALL. means at least one of them has to be reversed.
    So we have
    All cats are dogs. + Some dogs are are monkey : No need to go further.. As All+ Some= No conclusion which means that any possibility is true. So B is true
     

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