2) Use DeMorgan’s Laws to write the negation of the statement: “R≤min {m,n}". (hint: rewrite the statement as an “and” statement.)

Question

Been trying to figure out this problem, but I am completely clueless as to what to do. I know your suppose to use the quantifier and maybe an axiom.

Answer 1

Hi John,

Recall that DeMorgan's laws are about the complements of unions and intersections. The best way of thinking about this is that a union is tantamount to saying "or" and intersection is tantamount to saying "and."

For this problem, you need to find a way to write down the statement "R ≤ min {m, n}" in terms of sets.

This can be done by saying

"R ∈{x ∈ R | x ≤ m, x ≤ n},

where R denotes the real numbers. How can you rewrite the above set as a union or intersection? Now, negate it by taking the complement of the set and use DeMorgan's laws to get a statement for the negation.