Logical Statements :) By Dana, Mallory, and Jordan

Definitions

100

What is a hypothesis?

the part of the sentence following the "if".

200

what does Initial mean? P-hypothesis Q-conclusion

Initial-if P, then Q (if hypothesis, then conclusion) Converse-if Q, then P (if conclusion, then hypothesis)

300

what does converse mean? P-hypothesis Q-conclusion

Converse-if Q, then P (if conclusion, then hypothesis)

400

what does inverse mean? P-hypothesis Q-conclusion

Inverse-not P, then not Q (if not hypothesis, then not conclusion)

500

what does contrapositive mean? P-hypothesis Q-conclusion

Contrapositive- not Q, then not P (if not conclusion, then not hypothesis)

I,C,I,C

100

What is the converse to this initial statment: "If i go for a walk, then its sunny."

"If its sunny, then i'll go for a walk."

200

what it the contrapositive to this inverse? "if it's not raining, then i will go swimming."

"If i go swimming, then it's not raining."

300

what matching pairs go with each? Initial: ? Converse: ? Inverse: ? Contrapositive: ?

initial: contrapositive converse: inverse (vice versa)

400

what is the converse to this inverse statement? "If you don't eat your vegetables, then you won't grow."

"If you grow, then you ate your vegetables"

500

what is the contrapositive to this initial statement? "If a triangle is a right triangle, then it has a 90 degree angle."

"if a triangle doesn't have a 90 degree angle, then it is not a right triangle."

Biconditional Statements

100

is the statement below a true or false statement? also, does it even turned out to be a biconditional statement? "if you live in Memphis, then you live in Tennessee."

FALSE / NO- if you write the converse, it states "if you live in Tennessee, then you live in Memphis."

200

what words do you HAVE to have in a biconditional statement?

IF AND ONLY IF

300

what is the biconditional statement? "if an angle measures 90 degrees, then it is a right angle." "if its a right angle, then its 90 degrees."

an angle measures 90 degrees IF AND ONLY IF its a right angle.

400

what is the biconditional statement: Hypothesis: i am employed. Conclusion: i have a job Converse: "if i have a job, then i am employed."

"i am employed IF AND ONLY IFi have a job."

500

Does this inverse eventually turn into a biconditional statement? "if a quadrilateral is a rectangle, then it has 4 right angles."

TRUE/YES

Conclusions/ Conjectures

100

What does conclusion mean?

the result following the "then"

200

if its an apple, then its a fruit. what is the conclusion?

its a fruit...NOT THEN its a fruit

300

what is a conjecture?

a concluding statement using basic reasoning.

400

if it meows,purrs,and its fluffy, then..." what is the conclusion to this statement?

its a kitty cat or cat or kitty or etc.

500

i will go for a walk, if its sunny. what is the conclusion to this statement?

i will go for a walk. Try fliping it.