Some General Properties

Question 1

Addition property of equality.

Answer 1

(a = b) ⇒ (a + c = b + c)

Question 2

Subtraction property of equality.

Answer 2

(a = b) ⇒ (a - c) = (b - c)

Question 3

Multiplication property of equality.

Answer 3

(a = b) ⇒ (a * c = b * c)

Question 4

Division property of equality.

Answer 4

(a = b ∧ c ≠ 0) ⇒ (a/c = b/c)

Question 5

Reflexive property of equality.

Answer 5

a = a

Question 6

Symmetric property of equality.

Answer 6

(a = b) ⇒ (b = a)

Question 7

Distributive property of equality.

Answer 7

a * (b + c) = ab + ac

Question 8

Substitution property of equality.

Answer 8

(a = b) ⇒ (a replaces b in any equation)

Question 9

Transitive property of equality.

Answer 9

(a = b ∧ b = c) ⇒ (a = c)

Question 10

Addition property of inequality.

Answer 10

(a > b) ⇒ (a + c > b + c)

Question 11

Subtraction property of inequality.

Answer 11

(a > b) ⇒ (a - c > b - c)