The negation of proposition

Question

The negation of proposition "x≠0 and y≠0" is  "x[blank]0, [blank], y[blank]0"

 

Please fill in the blanks. Also, could you explain what negation of proposition is? I am not a native English speaker so this sounds a little bit confusing. I appreciate for help.

Answer 1

The negation of proposition "x≠0 AND y≠0" is "x = 0 OR y = 0"

 

(But this is not an exclusive "OR".)  This is an example of DeMorgan's laws.  You have a conjunction (AND) of propositions.  The negation of the conjunction is a disjunction (OR) of the negations.

 

"x ≠ 0" is a proposition

"y ≠ 0" is a proposition

 

"x ≠ 0 AND y ≠ 0" is the conjunction of the two.

 

"x = 0" is the negation of "x ≠ 0"

"y = 0" is the negation of "y ≠ 0"

 

"x = 0 OR y =0" is the disjunction of the two negations, and hence is it the negation of "x≠0 AND y≠0".