Logical Relations Between Propositions

Question 1

Define logical implication.

Answer 1

A proposition X logically implies a proposition Y if when X is true, then Y cannot be false.

Question 2

Define logical equivalence.

Answer 2

Propositions X and Y are logically equivalent if
1) When X is true, Y cannot be false.
and
2) When Y is true, X cannot be false.

Question 3

Define contradiction.

Answer 3

Propositions X and Y are contradictions of each other if
1) When X is true, Y cannot be true.
and
2) When X is false, Y cannot be false.

Question 4

Define contrariety.

Answer 4

Propositions X and Y are contraries of each if
1) X and Y cannot both be true.
and
2) X and Y can both be false.

Question 5

Define subcontrariety.

Answer 5

Propositions X and Y are contraries of each if
1) X and Y can both be true.
and
2) X and Y cannot both be false.

Question 6

Define subalternation.

Answer 6

Proposition X is the superaltern of a proposition Y if
1) When X is true, Y cannot be false.
and
2) When Y is true, X can be false.

Question 7

Define independence.

Answer 7

Propositions X and Y are independent of each if
1) When X is true, Y can be true.
2) When X is true, Y can be false.
3) When X is false, Y can be true.
and
4) When X is false, Y can be false.

Question 8

Define consistency.

Answer 8

Propositions X and Y are consistent with each other if X and Y can both be true.

Question 9

Define inconsistency.

Answer 9

Propositions X and Y are inconsistent with each other if X and Y cannot both be true.