Paper 2 Notes Flashcards
what is a statement?
must be true or false
* cannot be false, eg: non- statments : 5y+ 3= 14
what is the truth value of a statement?
the true/ false outcome of a statement:
* eg: 2 is even truth value = true
* 2 is odd, truth value = false
what does it mean to be logically equivalent?
the two statments have the same truth values in the same circumstances
draw a truth table for
* not (A)
* (B) and (A)
* (B) or (A)
Draw truth table for not A or B
- property of not is that it applies to what is immediately after : (not A ) or B
Draw the truth table for if A then B
Same for:
B if A
A only if B
if you take out the trash, then you get a dollar.
If human, then mamal
Draw the Venn Diagram for if A then B
Same for:
B if A
A only if B
(If you are in the shaded area it is true)
Draw the truth table for A if and only if B (A iff B)
Same as
B iff A
Draw the Venn Diagram for A iff B
Same as
B iff A
Draw a combined truth table for :
If A then B
If B then A
A only if B
B only if A
A iff B
B iff A
What is the converse of the following?
Just swap
What is the contra positive of the following?
Swap the two and then negate
What do these following statements become ?
Draw the Diagram for A is sufficient for B
Sufficient means inside the venue diagram
Draw the diagram for A is necessary for B
Necessary means the outer circle in the venn diagram
Complete the statements and use notation
What are the following statements equivalent to?
What is the general structure for simple deductive proofs?
What is the general structure for proof by contradiction?
What is the general structure of proof by contra positive
Find the contrapositive of the statement and then prove this by direct proof (if … then)
what are some problems that squaring introduces?
looking at proofs
squaring introduces additional solutions that must be checked
what must always be done when square rooting?
putting a +- before the square root so that we are not elimating solutions
what is wrong with diving expressions by some unknown?
what is the unknown = 0 then it will not be true
what is wrong with squaring both sides of an inequality?
-5 < 3
will not always be true becuase what is one side of the inequality was negative
25< 9 ?
if A > B then, sin A > sin B
cannot just take a function of both sides, this doesn’t always work
Determine whether the following statements are true
Determine whether the following statements are true
What are other worded way to say these phrases (necessary and sufficient)?
What about these following statements?
Is being odd necessary or sufficient to be prime?
Not sufficient, coz eg:9
Not necessary, coz eg: 2
What must you think / do when it comes up with the phrase “which of the following must be true /are necessarily true” ?
Try come up with counter examples that don’t use the condition yet still prove the statement correct
What must you do when deciding whether something is sufficient? (If…. Then ..) format
Find a counter example for when the first part is true BUT then the second part is not true.
How do you chose counter example for if then statements?
Must be true for the first if condition and then false for the then condition
what are some tips to coming up with counterexamples?
- go as trivial as possible
- use edge cases ( negatives/ fractions/ decimals)
