Symbolic
p->q
conditional
If a polygon is equiangular, then all its interior angles have the same measure.
If a polygon isn't equiangular, then all its interior angles don't have the same measure.
If Andres eats peanuts, then he will break out in hives.
If Andres breaks out in hives, then he has eaten peanuts.
If a polygon is equiangular, then all its interior angles have the same measure.
If all a polygon's interior angles don't have the same measure, then it isn't equiangular.
True or False:
If
p->q
q->r
r->s
Then
p->s
True
~q->~p
contrapositive
If it's Halloween, then I'm trick-or-treating.
If it's not Halloween, then I'm not trick-or-treating.
If two lines are parallel, then they have the same slope.
If two lines have the same slope, then they are parallel.
If one figure can be mapped onto another using rigid motions, then the two figures are congruent.
If two figures aren't congruent, then one can't be mapped onto the other using rigid motions.
True or False:
If
a->b
b->c
d->e
Then
a->e
False
q->p
converse
If a quadrilateral has two pairs of parallel sides, then it's a parallelogram.
If a quadrilateral doesn't have two pairs of parallel sides, then it's not a parallelogram.
If I find a dollar on the street, then I try to find out who it belongs to.
If I try to find out who a dollar belongs to, then I found it on the street.
If it's snowing, then Kennedy wears a coat out.
If Kennedy doesn't wear a coat out, then it's not snowing.
If Mr. Jones is mad, then a student upset him.
If a student upset him, then the student got a referral.
If the student got a referral, then the student got in trouble.
If Mr. Jones is mad, What can we conclude?
If Mr. Jones is mad, then a student got in trouble.
~p->~q
inverse
If everything goes just right, then today will be a good day.
If everything doesn't go just right, then today won't be a good day.
If it's a leap year, then February has 29 days.
If February has 29 days, then it's a leap year.
If my favorite song comes on the radio, then I sing along.
If I don't sing along, then my favorite song doesn't come on the radio.
If you eat pizza, then you will get fat.
If you get fat, then you are unhealthy.
If you are unhealthy, then you might die.
If you are a ghost, then you will haunt Mr. Jones.
What is a true conclusion?
If you eat pizza, then you might die.
p if and only if q
bi conditional
If two lines are perpendicular, then they intersect at right angles.
If two lines are perpendicular, then they intersect at right angles.
If it's an alien invasion, then you should run and hide.
If you should run and hide, then it's an alien invasion.
If it's an alien invasion, then you should run and hide.
If you shouldn't run and hide, then it's not an alien invasion.
If I study math, then I will pass my quiz tomorrow.
If I pay attention in class, then I will pass my quiz tomorrow.
If I pay attention in class, then I will get smart.
What is a true conclusion statement?
If I study math, then I will get smart.