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Blast into Math! Pure mathematics: the proof of the pudding is in the eating
Definition 2.3.1. In a statement of the form A implies B, A is the hypothesis, and B is the conclusion. A
implies B means:
Whenever the hypothesis A is true, then the conclusion B must also be true.
In mathematics and logic we use the arrow of implication =⇒ which means: whatever is at the tail of
the arrow implies whatever is at the tip of the arrow. So,
A =⇒ B meansexactly thesamething as AimpliesB.
Exercise: Have some fun with your new mathematical friend =⇒ while keeping its meaning in mind:
A =⇒ B means that whenever A is true, then B is also true. Practice writing A =⇒ B with A
and B in different positions but always with the same meaning. For example B ⇐ A . Get creative! A
could be above B, or A could be below B, but in all positions, A is at the tail of the arrow and B is at
the tip of the arrow.
Associated to a statement of the form A implies B is its converse.
Definition 2.3.2. The converse of the statement A implies B is the statement B implies A.
If we use the symbol =⇒ , then the converse of A =⇒ B is
B =⇒ A.
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