Definitions for proofs

Question 1

Conditional statement

Answer 1

P implies Q

Question 2

Converse

Answer 2

Q implies P - interchange hypothesis and the conclusion. Conditional statement is true does not mean converse is true.

Question 3

Negation

Answer 3

Opposite meaning to the conditional statement. If P then not Q

Question 4

Contrapositive

Answer 4

Truth of statement is the same as the conditional statement. Negation of Q implies the negation of P. If not Q then not P

Question 5

De Morgans Laws

Answer 5

States the negation of and is or

Question 6

Equivalent

Answer 6

If the converse is also true to the condition statement them statements are equivalent. P iff Q. P<>Q

Question 7

Counter example

Answer 7

Proves a statement as not true. E.g prove statement as false then the statement is therefore not true for all real numbers.

Question 8

Prove statement as true

Answer 8

Use algebra or odds and evens rules or prove negation as not true with a counter example

Question 9

Quantifier

Answer 9

Includes ‘there exists’ or a ‘for all’ statement

Question 10

Existential quantifier

Answer 10

‘There exists’. Claims that the statement holds true for at least one member of a given set. By showing the existence of such item, can prove the statement as true.

Question 11

Universal quantifier

Answer 11

Claims that the statement holds true for all members in a set. Need 1 counter example to prove the statement as wrong.

Question 12

Negation of a quantifier.

Answer 12

Interchange ‘For all’ with ‘There exists’ and then negate the rest of the statement. If prove the negation then you disprove the statement.

Question 13

Cos 45

Answer 13

root 2/2

Question 14

Tan 60

Answer 14

root 3

Question 15

sine 30

Answer 15

1/2

Question 16

13^2

Answer 16

169

Question 17

14^2

Answer 17

196

Question 18

15^2

Answer 18

225

Question 19

Inverse

Answer 19

If not P then not Q