Section 2

Question 1

Meaning of if a then b

Answer 1

If a is true then b is true. If a is false then b can be either true or false

Question 2

a only if b

Answer 2

can only be false if a is true and b is false. logically equivalent to if a then b

Question 3

a if and only if b

Answer 3

the same thing as[ (if a then b) and (if b then a) ] b and a can only be true in the same circumstances and false in the same circumstances

Question 4

a if b

Answer 4

logically equivalent to if b then a

Question 5

converse

Answer 5

swaps a and b. a statement and its converse are only equivalent in the case of a iff b

Question 6

contrapositive

Answer 6

a and b are swapped and negated. statement and contrapositive are equivalent in the case of a only if b

Question 7

a is necessary for b

Answer 7

if a is necessary for b then if b then a is true. when b is true then a is true and if a is false then b is false aswell. if b is false then a could be true or false

Question 8

a is sufficient for b

Answer 8

a is sufficient for b means the same thing as if a then b, so if a is true then b is true but if a is false b can be true or false.

Question 9

convex graph

Answer 9

f’‘(x)>0

Question 10

Root of a^2 equals

Answer 10

mod a not a