# Finding the fundamental conjuction

• Jan 6th 2013, 10:16 AM
mizzlizzym
Finding the fundamental conjuction
Find the fundamental conjunction made up from the variables w, x, y, z, or their complements, where the value of the conjunction is 1 precisely when:

w=x=0, y=z=1

So is this question asking us to find an equation that would equal 1 and at the same time use (in this question) w=x=0 and y=z=1?

Would notX(y)+ yz work? notx(y)= 1(1) and y(z)= 1(1) 1+1=1
• Jan 6th 2013, 11:32 AM
Deveno
Re: Finding the fundamental conjuction
you want an expression which is 1 ONLY when w = x = 0, y = z = 1, and for no other possible values of w,x,y,z.

furthermore, if this is only to be a conjunction terms like yz aren't allowed, so what you want is:

~w & ~x & y & z
• Jan 7th 2013, 03:04 PM
mizzlizzym
Re: Finding the fundamental conjuction
Okay I think I understand now. If we had the next example: w=0, x=y=z=1 would this work out?

w or x or y or z
w=0, 1 or 1 or 1= 1
simplifying it would be 0 or 1 equals 1
• Jan 7th 2013, 03:35 PM
emakarov
Re: Finding the fundamental conjuction
Quote:

Originally Posted by mizzlizzym
w or x or y or z

This disjunction is also true when w = x = y = 0 and z = 1 as well as for many other combinations of truth values.