Is the expression x space logical or space (y space logical and space z )equivalent to (x space logical or space y )space logical and space (x space logical or space z )for all possible inputs of x, y, and z

To prove:

X+Y.Z=(X+Y).(X+Z)

Taking R.H.S

= (X+Y).(X+Z)

By distributive law

= X.X+X.Z+X.Y+Y.Z --- (1)

From Boolean algebra

X.X = X

X.Y+X.Z = X.(Y+Z)

Using these in (1)

=X+X(Y+Z)+Y.Z

=X(1+(Y+Z)+Y.Z --- (2)

As we know (1+X) = 1

Then (2) becomes

=X.1+Y.Z

=X+Y.Z

Which is equal to R.H.S

Hence proved,

X+Y.Z=(X+Y).(X+Z)

answer   download the app called socratic on your phoner:

step-by-step explanation:

3

step-by-step explanation:

in standard form:

a= dictionaries

b= maps

you have to buy 3 dictionaries, so put a 3 next to the a (dictionaries) so that you can multiply them by each other.

a3+b= 60 (the amount of money you have)

we already know the cost of a=15 so replace a with $15

($15 x 3)+b=60

multiply 15 and 3 to get $45 and replace it with $45

45+b=60

and then replace b with 15 to get the total:

45+15=60

that means you have $15 left after buying 3 dictionaries.

15 divided by the cost of a map ($5) equals 3.

so you can buy 3 maps.

sorry if it was confusing!