Who can solve this of math question? (logical question)
[p ^ ( p' v q ) ]' v q
Which is the most simple way?
a) 1 b) 0 c) p v q d) p ^ q e) q.

. answer ; [ p ^ (p' v q )]' v q = [ p' v (p' v q)'] v q , ( De Morgan ) .....................................

= [ p' v ((p')' ^ q') ] v q ...............................................................................................

= [ p' v (p ^ q' ) ] v q , (distributive property) ................................................................

= [(p' v p) ^ ( p' v q')] v q ...........................................................................................

= [ 1 ^ ( p' v q' )] v q .................................................................................................

= (p' v q' ) v q , (coupling) .........................................................................................

= p' v ( q' v q ) ........................................................................................................

= p' v 1 .................................................................................................................

== 1 // .................................................................................................................

Question

Who can solve this of math question? (logical question)
[p ^ ( p' v q ) ]' v q 
Which is the most simple way?
a) 1        b) 0        c) p v q        d) p ^ q        e) q.

. answer ; [ p ^ (p' v q )]' v q = [ p' v (p' v q)'] v q , ( De Morgan ) .....................................

= [ p' v ((p')' ^ q') ] v q ...............................................................................................

= [ p' v (p ^ q' ) ] v q , (distributive property) ................................................................

= [(p' v p) ^ ( p' v q')] v q ...........................................................................................

= [ 1 ^ ( p' v q' )] v q .................................................................................................

= (p' v q' ) v q , (coupling) .........................................................................................

= p' v ( q' v q ) ........................................................................................................

= p' v 1 .................................................................................................................

== 1 // .................................................................................................................

Answer

Imagine that p and q are circles that overlap. It's useful to draw a series of pictures and darken the parts we want.

The innermost parenthesis consists of everything that is either not p or is q. So it consists of everything except that part of circle p that doesn't overlap with q.

The next innermost parenthesis consists of what we've just determined that is also in p. That's just the overlapping parts of p and q.

That is inversed, so we now have everything except the overlapping parts of p and q.

Finally we want everything that is either outside the overlapping parts or is in q. That's everything.

So your answer is a)

Answer

answer ; [ p ^ (p' v q )]' v q = [ p' v (p' v q)'] v q , ( De Morgan ) .........................................................................................
= [ p' v ((p')' ^ q') ] v q .........................................................................................
= [ p' v (p ^ q' ) ] v q , (distributive property) .....................................
= [(p' v p) ^ ( p' v q')] v q .........................................................................................
= [ 1 ^ ( p' v q' )] v q .........................................................................................
= (p' v q' ) v q , (coupling) .........................................................................................
= p' v ( q' v q ) .........................................................................................
= p' v 1 .........................................................................................
== 1 // .........................................................................................

Answer

answer ;
[ p ^ (p' v q )]' v q = [ p' v (p' v q)'] v q , ( De Morgan )
= [ p' v ((p')' ^ q') ] v q
= [ p' v (p ^ q' ) ] v q , (distributive property)
= [(p' v p) ^ ( p' v q')] v q

= [ 1 ^ ( p' v q' )] v q 

= (p' v q' ) v q , (coupling)

= p' v ( q' v q )

= p' v 1

== 1 //

Answer

@Liz : it is math question :) but logical...
.
.
@dnurfiani : ~p and p' same just different write :)

Answer

have no idea... what's that??