Syllogism

In each of the question below are three statements following by three conclusions numbered I, II and III. You have to take the three given statements to be true even if they seem to be at variance with commonly known facts and then decide which of the given conclusion logically follows from the two statements disregarding commonly known fact.

  1. Statement:
    All pins are rods. Some rods are chains. All chains are hammers.
    Conclusions:
    I. Some pins are hammers.
    II. Some hammers are rods
    III. No pin is hammer.
    1. Only I follows
    2. Only II follows
    3. Only III follows
    4. Only either I or III & II follows
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    All pins are rods + Some rods are chains = A + I = No conclusion Hence I and III does not follow. However, the two a complementary I-E pair, Hence either I or III follows. Some rods are chains + All chains are Hammers = I + A + I = Some rods are hammers → conversion → Some hammers are rods (I). Hence II follows.

    Correct Option: D

    All pins are rods + Some rods are chains = A + I = No conclusion Hence I and II does not follow. However, the two a complementary I-E pair, Hence either I or III follows. Some rods are chains + All chains are Hammers = I + A + I = Some rods are hammers → conversion → Some hammers are rods (I). Hence III follows.

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  1. Statement:
    Some books are papers. Some papers are desks. All desks are chairs.
    Conclusions:
    I. Some books are desks.
    II. Some papers are chairs.
    III. Some books are chairs.
    1. None follows
    2. Only I follows
    3. Only II follows
    4. Only III follows
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    I-type statements can't be combined.

    Correct Option: A

    I-type statements can't be combined.

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  1. Statement:
    Some pots are buckets. All buckets are tubs. All tubs are drums.
    Conclusions:
    I. Some drums are pots.
    II. All tubs are buckets.
    II Some drums are buckets.
    1. Only I and II follows
    2. Only I and III follows
    3. Only II and III follows
    4. All follows
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    All buckets are tubs(A) → conversion ⇒ Some tubs are buckets (I) Hence II does not follow. All buckets are tubs + All tubs are drums A + A = A = All buckets are drums → conversion → Some drums are buckets + All buckets are drums = A + A + I + = Some drums are pots(I). Hence II follows.

    Correct Option: B

    All buckets are tubs(A) → conversion ⇒ Some tubs are buckets (I) Hence II does not follow. All buckets are tubs + All tubs are drums A + A = A = All buckets are drums → conversion → Some drums are buckets + All buckets are drums = A + A + I + = Some drums are pots(I). Hence II follows.

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  1. Statement:
    All pins are bags. All chalks are bags. All needles are bags.
    Conclusions:
    I. Some needles are pins.
    II. Some chalks are needles.
    III. No needle is pin.
    1. Only I follows
    2. Only III follows
    3. Only either I or III follows
    4. Only either I or III and II follows
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    All pins are bags (A) → conversion → Some bags are pins (I). All needles are bags + Some bags are pins = A + I = No conclusion Hence I and III do not follow by combination. However, they from an complementary E-I pair, either I or III follows. Again, All chalks are bags + conversion of all needles are bags = A + I = No conclusion Hence II do not follow.

    Correct Option: C

    All pins are bags (A) → conversion → Some bags are pins (I). All needles are bags + Some bags are pins = A + I = No conclusion Hence I and III do not follow by combination. However, they from an complementary E-I pair, either I or III follows. Again, All chalks are bags + conversion of all needles are bags = A + I = No conclusion Hence II do not follow.

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  1. Statement:
    Some buses are trucks. Some trucks are boats. No boat is jeep.
    Conclusions:
    I. Some jeeps are buses.
    II. Some boats are buses.
    III. Some jeeps are trucks.
    1. None follows
    2. Only I follows
    3. Only II follows
    4. Only III follows
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    Some buses are trucks + Some trucks are boats = I + I = No conclusion Hence II and consequently do not follow Some trucks are boats + No boat is jeep = I + E = O = Some trucks are not jeeps. Hence III does not follow.

    Correct Option: A

    Some buses are trucks + Some trucks are boats = I + I = No conclusion Hence II and consequently do not follow Some trucks are boats + No boat is jeep = I + E = O = Some trucks are not jeeps. Hence III does not follow.

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