properties of equality and real numbers

Question 1

a=a

Answer 1

reflexive property

Question 2

a=b —> b=a

Answer 2

symmetric property

Question 3

(a = b /\ b = c) —> a=c

Answer 3

transitive property

Question 4

a=b —> 3a + 1 = 3b + 1

Answer 4

substitution property

Question 5

a=b —> a+c = b+c

Answer 5

addition property

Question 6

a=b —> a-c = b-c

Answer 6

subtraction property

Question 7

a=b —> a/c = b/c

Answer 7

multiplication property

Question 8

a=b —> a/c = b/c

Answer 8

division property

Question 9

a=b —> a2 = b2

Answer 9

exponent property

Question 10

a=b —> -/a = -/b

Answer 10

square root property

Question 11

a+b +c —> b+ a + c

Answer 11

commutative property of addition

Question 12

a x b x c —> b x a x c

Answer 12

commutative property of multiplication

Question 13

a+b (b+c) —> (a+b) + c

Answer 13

associative property of addition

Question 14

a - (b+c) —> (a+b) + c

Answer 14

associative property of multiplication

Question 15

a(b+c) —> ab + bc

Answer 15

distributive property

Question 16

a+0 = a

Answer 16

identity property of addition

Question 17

a-0 = a

Answer 17

identity property of subtraction

Question 18

a x 1 = a

Answer 18

identity property of multiplication

Question 19

a/1 = a

Answer 19

identity property of division

Question 20

a+(-a) = 0

Answer 20

additive inverse property

Question 21

a - (1/a) = 1

Answer 21

multiplicative inverse property