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# Use the algebra of propositions to pmve:

Hi there.

I'm having alot of problems trying to understand the steps (De Morgans, Distributive etc)

I have attempted but I am afraid I haven't gotten it at all.

i) (p v q) ^ ~p = q ^ ~p

LHS= (p v q) ^ ~p

= (p v ~p) ^ (q v ~p)

= T ^ (q v ~p)

= (q ^ ~p)

ii) ~(p ^(~p v q))= ~(p ^ q)

LHS= ~(p ^(~p v q))

= (~p) ^ (~p v ~q)

= ???

iii) ((p v q) ^ ~(p ^q)= p <->q

LHS= ((p v q) ^ ~(p ^q)

= p v q ^ (~p v ~q)

=(p v ~p) ^ (q v ~q)

=p <-> q

iv) ~(~p->~(p v q) = ~(q->p)

LHS= ~(~p->~(p v q)

=~~p -> ( ~p v ~q)

= (p v ~p) -> ~(p v q)

= T v ~ (p v q)

= ~p v q

Any help would be appreciated as I am struggling

Use the algebra of propositions to pmve: m {quhﬁpﬁqn—wp {In -{pn{~wq)}E-{PM} {In} —{(qu)»~4an)}5qu
{Iv} 41v —r—(pvq})E+(q —&gt;p)

The part a and c you did correctly. for part second you just extracted it incorrectly look here LHS =¬(p ﻿ ∧ ﻿ (¬p... View the full answer

• sorry in the middle pls read "fourth" in place of third.
• jhvivekrai
• Apr 02, 2018 at 3:29am
• I just realised I am missing the negation on the third question, that will obviously affect it yes?
• hugohenry
• Apr 02, 2018 at 3:48am
• yes. obviously
• jhvivekrai
• Apr 02, 2018 at 4:13am
• ¬((p∨q)∧¬(p∧q))=¬(p∨q)∨¬¬(p∧q)=(¬p∧¬q)∨(p∧q)=p⇔q﻿﻿.
• jhvivekrai
• Apr 02, 2018 at 7:05am
• it should be like this
• jhvivekrai
• Apr 02, 2018 at 7:06am
• you just missed the negation
• jhvivekrai
• Apr 02, 2018 at 7:13am

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