Perform the following modular arithmetic by applying the addition/subtraction rule. (a) (9+15) mod 7 (b) (15-23) mod 5 (c) (-47 x (5+1)) mod 5

Let us perform the following modular arithmetic by applying the addition/subtraction rule.

(a) $(9+15) \mod 7=(9\mod 7)+(15 \mod 7)=(2\mod 7)+(1 \mod 7)=3 \mod 7$

(b) $(15-23) \mod 5=(15 \mod 5)-(23 \mod 5)=(0 \mod 5)-(3 \mod 5)\\$

$=-3 \mod 5=2 \mod 5$

(c) $(-47 \cdot (5+1)) \mod 5 =(-47 \mod 5)\cdot ((5+1) \mod 5)$

$=(3 \mod 5)\cdot (1 \mod 5) =3 \mod 5$