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Using mathematical logic, we often find that statements that seem quite different on the surface are equivalent, which is to say, they have the same truth value under all distinguishable conditions. Or, to put it another way, if statement A is true in all and only the cases that statement B is true, they are equivalent.

One simple and basic case of two statements that are equivalent, but that may not look equivalent is "P implies Q"

P IMPLIES Q

and "Not-P or Q"

NOT P OR Q. Both

Both are true in all and only the cases where Q is true or P is false. This is because the way "implies"IMPLIES is defined (in logics such as the one you are studying), is as meaning that if P is true, Q must also be true (if P is false, Q can be either true or false), and the way OR is defined is as meaning that at least one of the two sides of the OR is true (but both can be).

In some ways, we might say that the whole purpose of mathematical logic is to go beyond the dictates of intuition in cases such as these.

Using mathematical logic, we often find that statements that seem quite different on the surface are equivalent, which is to say, they have the same truth value under all distinguishable conditions. Or, to put it another way, if statement A is true in all and only the cases that statement B is true, they are equivalent.

One simple and basic case of two statements that are equivalent, but that may not look equivalent is "P implies Q" and "Not-P or Q". Both are true in all and only the cases where Q is true or P is false. This is because the way "implies" is defined (in logics such as the one you are studying), is as meaning that if P is true, Q must also be true (if P is false, Q can be either true or false).

In some ways, we might say that the whole purpose of mathematical logic is to go beyond the dictates of intuition in cases such as these.

Using mathematical logic, we often find that statements that seem quite different on the surface are equivalent, which is to say, they have the same truth value under all distinguishable conditions. Or, to put it another way, if statement A is true in all and only the cases that statement B is true, they are equivalent.

One simple and basic case of two statements that are equivalent, but that may not look equivalent is

P IMPLIES Q

and

NOT P OR Q.

Both are true in all and only the cases where Q is true or P is false. This is because the way IMPLIES is defined (in logics such as the one you are studying), is as meaning that if P is true, Q must also be true (if P is false, Q can be either true or false), and the way OR is defined is as meaning that at least one of the two sides of the OR is true (but both can be).

In some ways, we might say that the whole purpose of mathematical logic is to go beyond the dictates of intuition in cases such as these.

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source | link

Using mathematical logic, we often find that statements that seem quite different on the surface are equivalent, which is to say, they have the same truth value under all distinguishable conditions. Or, to put it another way, if statement A is true in all and only the cases that statement B is true, they are equivalent.

One simple and basic case of two statements that are equivalent, but that may not look equivalent is "P implies Q" and "Not-P or Q". Both are true in all and only the cases where Q is true or P is false. This is because the way "implies" is defined (in logics such as the one you are studying), is as meaning that if P is true, Q must also be true (if P is false, Q can be either true or false).

In some ways, we might say that the whole purpose of mathematical logic is to go beyond the dictates of intuition in cases such as these.