Conditional Statements
Rewrite the biconditional as a conditional statement and its converse: Darth Vader is your father if and only if you are Luke.
What is conditional: If Darth Vader is your father, then you are Luke. converse: If you are Luke, then Darth Vader is your father.
P: Troy likes football ~P
What is Troy doesn't like football.
Solve and give reasons: 3x-11=23
What is 3x=24 (addition) x=11.3 (division)
See Proof 1 - Complete Reason 1.
What is "given."
What is the hypothesis in the following statement: If cookies are good, then Mr. McMahon bakes cookies.
What is If cookies are good.
Determine if this biconditional is true. If false provide a counterexample: x=4 if and only if x+9=13
What is True
P: Whales swim in water Q: Birds fly in the air ~P->Q
What is If whales don't swim in water, then birds fly in the air.
Solve for x and give reasons: 7x+34=-9x+66
What is 16x+34=66 (addition) 16x=32 (subtraction) x=2 (division)
See Proof 1 - Complete Reason 2.
What is definition of Complementary.
What is the conclusion of the following statement: If snow is cold, then water isn't wet.
What is then water isn't wet.
Given the conditional statement, write the converse and the biconditional. Conditional: If pens write, then ducks quack.
What is Converse: If ducks quack, then pens write. Biconditional: Pens write if and only if ducks quack.
P: Wizards are real Q: Sharks fly in space P <--> Q
What is Wizards are real if and only if sharks fly in space.
Solve for x and give reasons: 3(x-5)+22=5x-19
What is 3x-15+22=5x-19 (distributive) 3x+7=5x-19 (combine like terms) -2x+7=-19 (subtraction) -2x=-26 (subtraction) x=13 (division)
See Proof 1 - Complete Reason 3.
What is the "given."
Converse: If Adam likes apples, then penguins fly. Determine the conditional statement that goes with this statement.
What is If penguins fly, then Adam like apples.
Determine if this biconditional is true. If false provide a counterexample: x=4 if and only if x^2=16
What is False: if x^2=16, then x=-4 works as well.
P: Eric mines for gold Q: Pirates don't have fun
Q <--> P
What is Eric mines for gold if and only if pirates don't have fun.
Solve for x and give reasons AB=x+5, CD=3x-9, AB=EF and EF=CD
What is AB=CD (transitive) x+5=3x-9 (substitution) x=3x-14 (subtraction) -2x=-14 (subtraction) x=7 (division)
See Proof 1 - Complete Reason 4.
What is substitution.
Statement: If puppies aren't cute, then the sky is blue. Determine the converse.
What is Converse: If the sky is blue, then puppies aren't cute.
Given a true conditional statement, determine if the converse is also true. Conditional: If there is a seal, then it lives in the ocean.
What is the converse: If it lives in the ocean, then it is a seal. False
Statement P and Q are the hypothesis and conclusion of the following conditional statement. If dogs lay eggs, then cats bark. Write the biconditional statement of this conditional statement.
What is Dogs lay eggs if and only if cats bark.
Solve for x and give reasons: If B is the midpoint of AC, and AB=3x+9 and AC=9x-84
What is AC=AB+BC (segment addition) AB=BC (definition of midpoints) AC=AB+AB (substitution) 9x-84=3x+9+3x+9 (substitution) 9x-84=6x+18 (combine like terms) 3x-84=18 (subtraction) 3x=102 (addition) x=34 (division)
See Proof 1 - Complete Reason 5.
What is Subtraction POE.