Hello, i am trying to solve a problem of discrete math and i am having a lot of problem with it. if someone could help me please
The exercise is the following:
If A,B,C are sets, then show that
A X (B U C) = (A X B) U (A X C)
Thanks!!
Hello, i am trying to solve a problem of discrete math and i am having a lot of problem with it. if someone could help me please
The exercise is the following:
If A,B,C are sets, then show that
A X (B U C) = (A X B) U (A X C)
Thanks!!
The statement that $\displaystyle (x,y)\in A\times (B\cup C)$ means that $\displaystyle x\in A~\&~y\in (B\cup C)$.
The statement that $\displaystyle (x,y)\in[( A\times B)\cup(A\times C)]$ means that $\displaystyle (x,y)\in(A\times B)\text{ or }(x,y)\in(A\times C)$.
Now you show those to are equivalent.
Here is the proof: $\displaystyle (x \in A) \wedge \left[ {y \in B \vee y \in C} \right] \Leftrightarrow \left[ {\left( {x \in A \wedge y \in B} \right) \vee \left( {x \in A \wedge y \in C} \right)} \right]$.
If you know the meaning of cross product and you read my first reply, then it should be clear to you.