Class Notes (835,894)
Canada (509,478)
Mathematics (458)
MA100 (21)

Elements of logic this is the second days notes and covers contrapositives, hypothesis, converses, ect.

3 Pages
Unlock Document

Shane Bauman

Elements of Logic In mathematics a statement is a declarative sentence that can be true or false but not both. Ex. 7 is a prime number – true Ex. (-3, 4] εŽ – false A mathematical identity is an equality relation that is always true for all values of the variable in the relation. Ex. (x+3) = x + 6x + 9 Ex. Sin θ + cos θ = 1 An equation is an equality relation depending on some variables for which we are asked to find all values that make the statement true. Ex. Solve x(x+3) – 3(x+2) = 0 Clearly not an identity since for x=0  -6=0 2 X +3x-3x-6=0 X =6 X=±√6 – you can always check by substituting. Solution: {-√6, √6} (read (2) what is mathematics? Proof and solutions) Proofs: 1) identities LS=RS Ex. Prove ( )( ) ( ) ( )( ) 2) hypothesis/conclusion Ex. “I think therefore I am” “if a triangle is equilateral then all interior angles are 60⁰ Ex. Prove that if m and n are even numbers then m+n is also even Proof: givens: m, n are even  m=2s, n=2t s,tεŽ  m+n= 2s+2t= 2(s+t) e e The converse of a statement is a statement obtained by switching the hypothesis with the conclusion Ex. I think therefore I am Converse: I am therefore I think If a statement is true it is not always guaranteed that its converse is true. Ex. If m+n is even it is not guaranteed that m, n are even. Counter example: 8=3+5 3) Equivalent statements How
More Less

Related notes for MA100

Log In


Join OneClass

Access over 10 million pages of study
documents for 1.3 million courses.

Sign up

Join to view


By registering, I agree to the Terms and Privacy Policies
Already have an account?
Just a few more details

So we can recommend you notes for your school.

Reset Password

Please enter below the email address you registered with and we will send you a link to reset your password.

Add your courses

Get notes from the top students in your class.