Posted by Julie on Thursday, December 9, 2010 at 10:35pm.
“A 150° angle is an obtuse angle.”
We will represent the proposition as follows:
p=the angle is 150°
q=it is an obtuse angle
The above proposition (may or may not be true) is equivalent to:
p->q (If the angle is 150°, it is an obtuse angle).
The converse is
q->p (If an angle is obtuse, it is 150°)
The biconditional is:
p<->q (If the angle is 150°, it is an obtuse angle, and if an angle is obtuse, it is 150°)
We can see that p->q is true, but q->p is not. Consequently p<->q is not true, because
p<->q ≡ p->q ∧ q->p,
so if q->p is false, p<->q is also false.
The Euler diagram for p->q is a small circle P completely inside a bigger circle Q, so that whenever p is true, q has to be true.
Try to draw the Euler diagram for the other two cases.
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