Thread: logic statement

1. For [ ( p → q ) ʌ q ] → p make up the statement for p and one for q, then write a statement of this form in words to illustrate that this statement form is sometimes false.

2. The negation of statement form like pʌq can be written "not(pʌq)" or " it is false that pʌq" but these are considered trivial negations. A non trivial negation will change the form of the statement. For example using DeMorgans Law the negation of (pʌq) can be written (not p ᴠ not q). Using some of the logical equivalences on the tautology sheet write a non trivial negation of each of the following statements:

a) If roses are red then violets are purple.

b) Triangle ABC is isosceles or it is scalene

C) A figure is a parallelogram if and only if it is a rectangle. Please Help

Originally Posted by olenka

1. For [ ( p → q ) ʌ q ] → p make up the statement for p and one for q, then write a statement of this form in words to illustrate that this statement form is sometimes false.

2. The negation of statement form like pʌq can be written "not(pʌq)" or " it is false that pʌq" but these are considered trivial negations. A non trivial negation will change the form of the statement. For example using DeMorgans Law the negation of (pʌq) can be written (not p ᴠ not q). Using some of the logical equivalences on the tautology sheet write a non trivial negation of each of the following statements:

a) If roses are red then violets are purple.

b) Triangle ABC is isosceles or it is scalene

C) A figure is a parallelogram if and only if it is a rectangle. Please Help

Let .....p= i go to London and q= i buy a car ,hence :



I say If i go to London i will buy a car (p---->q) and so happens that i bought a car .........[(p---->q) ^ q] .Can we conclude then that i went to London???..................[(p---->q) ^ q]------>q???



.....................................NO................................................ .......

I COULD have bought the car in Paris

On the other hand if i say that:

if i go to London i will visit the Bloody Tower and it so happens that i did visit the Bloody Tower ,what can be said now ??

.............did or did not go to London??.......................................... ......


NOW for question 2 we have:

a) Let p=roses are red and q= violets are purple .The negation of p---->q (= if roses are red then violets are purple) is ~(p---->q), which is equivalent ~( ~pvq) which is equivalent to p^ ~q (=roses are red and the violets are not red).

So we say that,if it is not true that : if roses are red then violets are purple,then :roses are red and violets are not purple


b) the negation of "b" is that:

ABC is not isosceles and ABC is not scalene

For question "a" p--->q is equivalent to ~pvq and now the negation of that ~(~pvq) through De Morgan law is equivalent ...............p^~q

Thank you so much ...but what about problem 2c?

I AM sorry for the moment i got lost.


2c is a biconditional.

let p= S is para//gram and q= S is square then we have :

...................................p<------>q............................................1

and the negation of that is:

................................((~p& q) v(p& ~q)).......................................2

NOTE IN the above instead of "a figure" i used S.

Also .........................p<------->q is equivalent to ........[(p----->q)^(q------->p)]..................3

Now by negating 3 try to arrive to ..................................2

Thank you so much U R The BEST !!!!!