Discrete Mathematics

Question

Is the assertion "This statement is false." a proposition? Justify.

Answer 1

Call "This statement is false" P

if P is true, then P is false

If P is false, then P is true

It's a paradox,

By logic, it's a tautology that Pv~P and a contradiction if P&~P

If P then ~P is a contradiction.

If ~P then P is a contradiction

This statement is false is a contradiction.

maybe like light is a wave but also a particle or how quantum physics has been proven true and relativity has been proven true, but quantum physics contradicts relativity.

There's a barber in a small town. He cuts the hair of every resident who doesn't cut their own hair. Does the barber cut his own hair? He's a resident of the town. If he cuts his own hair then he can't cut his own hair

because he only cuts the hair of those who do not cut their own hair. Similar paradox.

Or maybe like Schodinger's cat. It's both alive and dead, before someone opens the box and looks at the cat.

As Cal Tech's experimental physicist Professor Leonard told Penny in an early episode, "Life is filled with contradictions as he explains her love/hate relationship with her ex-boyfriend.