Symbolic
p->q
conditional
If a triangle is equilateral, then all its sides have the same measure.
If a triangle isn't equilateral, then all its interior sides do not 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 triangle is equilateral, then all its sides have the same measure.
If a triangle's sides do not have the same measure, then it is not equilateral.
If p->q and q->r what can we conclude?
p->r
~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 are not congruent, then one can not be mapped onto the other using rigid motions.
If p->q and p is true, what can we conclude?
q is true
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 does not wear a coat out, then it is not snowing.
If a student is caught in the hallway without a pass, then they get a detention.
If a student gets a detention, then they must stay after school until 3:50.
If a student is caught in the hallway without a pass, then they must stay after school until 3:50.
~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 do not sing along, then my favorite song does not come on the radio.
If it is game day, then you eat pizza.
It is game day.
What can be concluded?
You eat pizza.
pharrq
bi conditional
If two lines are perpendicular, then they intersect at right angles.
If two lines are not perpendicular, then they do not 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.
What can be concluded?
No conclusion.