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Logical Connectives Test - 2

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Logical Connectives Test - 2
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  • Question 1
    3 / -1

    Statements:

    All fruits are vegetables. All pens are vegetables. All vegetables are rains.

    Conclusions:

    1. All fruits are rains.
    2. All pens are rains.
    3. Some rains are vegetables.

    Solution

    III is the converse of the third premise and so it holds.

    All fruits are vegetables. All vegetables are rains.

    The conclusion must be universal affirmative and should not contain the middle term.

    So, it follows that 'All fruits are rains'. Thus, I follows.

    All pens are vegetables. All vegetables are rains.

    Clearly, it follows that 'All pens are rains'. Thus, II follows.

  • Question 2
    3 / -1

    Statements: Some towels are brushes. No brush is soap. All soaps are rats.

    Conclusions:

    1. Some rats are brushes.
    2. No rat is brush.
    3. Some towels are soaps.

    Solution

    Explanation:

    Some towels are brushes. No brush is soap.

    Since one premise is particular and the other negative, the conclusion must be particular negative (O-type) and should not contain the middle term. So, it follows that 'Some towels are not soaps'. No brush is soap. All soaps are rats.

    Since the middle term is distributed twice, the conclusion must be particular. Since one premise is negative, the conclusion must be negative. So, it follows that 'Some brushes are not rats'. Since I and II involve the same terms and form a complementary pair, so either I or II follows.

  • Question 3
    3 / -1

    Statements: Some pictures are frames. Some frames are idols. All idols are curtains.

    Conclusions:

    1. Some curtains are pictures.
    2. Some curtains are frames.
    3. Some idols are frames.

    Solution

    Explanation:

    III is the converse of the second premise and so it holds.

    Some pictures are frames. Some frames are idols.

    Since both the premises are particular, no definite conclusion follows.

    Some frames are idols. All idols are curtains.

    Since one premise is particular, the conclusion must be particular and should not contain the middle term. So, it follows that 'Some frames are curtains'. III is the converse of this conclusion and so it holds.

    Some pictures are frames. Some frames are curtains.

    Since both the premises are particular, no definite conclusion can be drawn.

  • Question 4
    3 / -1

    Statements: Some hills are rivers. Some rivers are deserts. All deserts are roads.

    Conclusions:

     

    1. Some roads are rivers.
    2. Some roads are hills.
    3. Some deserts are hills.

    Solution

    Explanation:

    Some hills are rivers. Some rivers are deserts.

    Since both the premises are particular, no definite conclusion follows.

    Some rivers are deserts. All deserts are roads.

    Since one premise is particular, the conclusion must be particular and shouldn't contain the middle term. So, it follows that 'Some rivers are roads'. I is the converse of this conclusion and so it holds.

    Some hills are rivers. Some rivers are roads.

    Again, since both the premises are particular, no definite conclusion follows.

  • Question 5
    3 / -1

    Statements: Some saints are balls. All balls are bats. Some tigers are balls.

    Conclusions:

    1. Some bats are tigers.
    2. Some saints are bats.
    3. All bats are balls.

    Solution

    Explanation:

    Some saints are balls. All balls are bats.

    Since one premise is particular, the conclusion must be particular and should not contain the middle term. So, it follows that 'Some saints are bats'. Thus, II follows. Some tigers are balls. All balls are bats.

    Since one premise is particular, the conclusion must be particular and should not contain the middle term. So, it follows that 'Some tigers are bats'. I is the converse of this conclusion and so it holds.

  • Question 6
    3 / -1

    Statements: All tigers are jungles. No jungle is bird. Some birds are rains.

    Conclusions:

    1. No rain is jungle.
    2. Some rains are jungles.
    3. No bird is tiger.

    Solution

    Explanation:

    All tigers are jungles. No jungle is bird.

    Since both the premises are universal and one premise is negative, the conclusion must be universal negative (E-type) and should not contain the middle term.

    So, it follows that 'No tiger is bird'. III is the converse of this conclusion and so it holds.

    No jungle is bird. Some birds are rains.

    Since one premise is particular and the other negative, the conclusion must be particular negative (O-type) and should not contain the middle term. So, it follows that 'Some jungles are not rains'.

    Since I and II also involve the same terms and form a complementary pair, so either I or II follows.

  • Question 7
    3 / -1

    Statements: All snakes are trees. Some trees are roads. All roads are mountains.

    Conclusions:

    1. Some mountains are snakes.
    2. Some roads are snakes.
    3. Some mountains are trees.

    Solution

    Explanation:

    All snakes are trees. Some trees are roads.

    Since the middle term is not distributed even once in the premises, so no definite conclusion follows.

    Some trees are roads. All roads are mountains.

    Since one premise is particular, the conclusion must be particular and should not contain the middle term. So, it follows that 'Some trees are mountains'. III is the converse of this conclusion and so it holds.

    All snakes are trees. Some trees are mountains.

    Since the middle term is not distributed even once in the premises, so no definite conclusion follows.

  • Question 8
    3 / -1

    Statements: All trees are flowers. No flower is fruit. All branches are fruits.

    Conclusions:

    1. Some branches are trees.
    2. No fruit is tree.
    3. No tree is branch.

    Solution

    Explanation:

    All trees are flowers. No flower is fruit.

    Since both the premises are universal and one premise is negative, the conclusion must be universal negative (E-type) and should not contain the middle term. So, it follows that 'No tree is fruit'. II is the converse of this conclusion and so it follows.

    All branches are fruits. No flower is fruit.

    Since both the premises are universal and one premise is negative, the conclusion must be universal negative (E-type) and should not contain the middle term. So, it follows that 'No branch is flower'.

    All trees are flowers. No branch is tree.

    As discussed above, it follows that 'No tree is branch'. So, III follows.

    Hence, both II and III follow.

  • Question 9
    3 / -1

    Statements: Some uniforms are covers. All covers are papers. All papers are bags.

    Conclusions:

    1. All covers are bags.
    2. Some bags are covers, papers and uniforms.
    3. Some uniforms are not papers.

    Solution

    Explanation:

    Some uniforms are covers. All covers are papers.

    Since one premise is particular, the conclusion must be particular and should not contain the middle term. So, it follows that 'Some uniforms are papers'. All covers are papers. All papers are bags.

    Since both the premises are universal and affirmative, the conclusion must be universal affirmative (A-type) and should not contain the middle term. So, it follows that 'All covers are bags'. Thus, I follows. The converse of this conclusion i.e. 'Some bags are covers' also holds.

    Some uniforms are covers. All covers are bags.

    Since one premise is particular, the conclusion must be particular and should not contain the middle term. So, it follows that 'Some uniforms are bags', The converse of this conclusion i.e. 'Some bags are uniforms' also holds.

    Further, the converse of the third premise i.e. 'Some bags are papers' holds.

    Now, II is the cumulative result of the conclusions 'Some bags are covers', 'Some bags are papers' and 'Some bags are uniforms'. Thus, II follows.

  • Question 10
    3 / -1

    Statements: No rabbit is lion. Some horses are lions. All rabbits are tables.

    Conclusions:

    1. Some tables are lions.
    2. Some horses are rabbits.
    3. No lion is table.

    Solution

    Explanation:

    Some horses are lions. No rabbit is lion.

    Since one premise is particular and the other negative, the conclusion must be particular negative (O-type) and should not contain the middle term.

    So, it follows that 'Some horses are not rabbits'.

    All rabbits are tables. No rabbit is lion.

    Since the middle term 'rabbits' is distributed twice, the conclusion must be particular.

    Since one premise is negative, the conclusion must be negative. So, it follows that 'Some tables are not lions'. Since I and III involve the same terms and form a complementary pair, so either I or III follows.

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