Prove A minus B Intersect C Equals A minus B Union A minus C

[Princess Shaina]

Prove that
a-(b∩ c)=(a-b)u(a-c)

 

[I like Serena]

Prove that
a-(b∩ c)=(a-b)u(a-c)

Hello Your Highness! Welcome to MHB! ;)

Which rules for set manipulation can we use? (Wondering)

 

[physiclawsrule]

A-(B⋂C)=(A-B)⋃(A-C) If A-B={xlx∈A and x∉B} A-C={xlx∈A and x∉C} then (A-B)⋃(A-C)={xlx∈A, x∉(B and C) Let X=A and Y=(B⋂C) X-Y={xlx∈X and x∉Y} x∉Y x∉(B⋂C) x∉(B and C) physicsforums

 

[suluclac]

Have you tried using the Venn diagram?

 

[soroban]

Prove that
a-(b∩ c)=(a-b)u(a-c)

$$\begin{array}{ccccc} 1. & a - (b \cap c) && 1. & \text{LHS} \\ <br /> 2. & a \cap \overline{(b \cap c)} && 2. & \text{Def. subtr'n} \\ <br /> 3. & a \cap ( \overline b \cup \overline c) & & 3. & \text{DeMorgan} \\<br /> 4. & (a \cap{\overline b}) \cup (a \cap {\overline c}) && 4. & \text{Distributive} \\<br /> 5. & (a - b) \cup (a - c) && 5. & \text{Def. subtr'n} \\<br /> &&&& \text{RHS}\end{array}$$