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Conditional Statements
Biconditional Statements
Symbolic Notation
Algebra Proofs
100
Write the converse of the following: If Tom likes pizza, then Harry likes dogs.
What is If Harry likes dogs, then Tom likes pizza
100
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.
100
P: Troy likes football ~P
What is Troy doesn't like football.
100
Solve and give reasons: 3x-11=23
What is 3x=24 (addition) x=8 (division)
200
Write the inverse of the following: If cookies are good, then Mr. McMahon bakes cookies.
What is If cookies aren't good, then Mr. McMahon doesn't bake cookies.
200
Determine if this biconditional is true. If false provide a counterexample: x=4 if and only if x+9=13
What is True
200
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.
200
Solve for x and give reasons: 7x+34=-9x+66
What is 16x+34=66 (addition) 16x=32 (subtraction) x=2 (division)
300
Write the contrapositive of the following statement: If snow is cold, then water isn't wet.
What is If water is wet, then snow isn't cold.
300
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.
300
P: Wizards are real Q: Sharks fly in space P <--> ~Q
What is Wizards are real if and only if sharks don't fly in space.
300
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)
400
Converse: If Adam likes apples, then penguins fly. Determine what the conditional statement is and write the inverse.
What is If penguins don't fly, then Adam doesn't like apples
400
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.
400
P: Eric mines for gold Q: Pirates don't have fun R: Russians are cold a) P->~R b)~Q <--> ~P
What is a) If Eric mines for gold, then Russians aren't cold. b) Pirates have fun if and only if Eric doesn't mine for gold.
400
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)
500
Inverse: If puppies aren't cute, then the sky is blue. Determine the original conditional statement, and then write both the conditional, converse and contrapositive
What is Conditional: If puppies are cute, then the sky isn't blue. Converse: If the sky isn't blue, then puppies are cute. Contrapositive: If the sky is blue, then puppies aren't cute.
500
Given a true conditional statement, determine if the converse is also true. If yes, write the biconditional. If no, give a counterexample. Conditional: If there is a seal, then it lives in the ocean.
What is False: If there is an ocean, then sharks live in it.
500
Statement P and Q are the hypothesis and conclusion of the following conditional statement. Determine what P and Q are. If dogs lay eggs, then cats bark. Then write ~Q <--> P
What is Cats don't bark if and only if dogs lay eggs.
500
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)