contrapositive LG Forum

[senorhosh]

For grouping games:
Is it safe to assume that 100% of the time, a contrapositive can be made by reversing the arrows and slash marks?

For example:
A --> B (If A is chosen B is chosen)
Contrapositive:
B --> A (If B is not chosen, A is not chosen)

Or example #2
A --> B (if A is not chosen, B is chosen)
Contrapositive:
B --> A (If B is not chosen, A is chosen)

Seems like it's been working everytime. Before I start relying on this, are there instances when this is NOT true??

[Verity]

It's always true. It's a logical rule, it's not contingent on the game type.

[Campagnolo]

The contrapositive is always equivalent to the original statement, whether in the games section, the logical reasoning section, or any other time whatever.

Rely on it.

[EarlCat]

Flip, negate, swap "and" and "or."

[cogitoergosum]

I find it helpful to think of it this way:

Example 1:
A-->B: if A occurs, then B must occur

Contrapositive:
NOT B --> NOT A: If B does not occur, then it is not possible that A occurred (because if A had occurred, then we know from the original conditional statement above that B would have occurred)

Example 2:
A and B --> C: if both A and B occur, then C must occur

Contrapositive:
NOT C --> NOT A or NOT B (either A or B [or both] must not have occurred, because if both had occurred, then we know from the original conditional statement above that C would have occurred)

[joebloe]

The contrapositive is always equivalent to the original statement, whether in the games section, the logical reasoning section, or any other time whatever.

Rely on it.

This. By the time you hit test day, you should be able to form a contrapositive in your sleep, and should be doing it automatically whenever a question seems to contain logical implications.