discrete mathematics - Prove or Disprove quantifiers (propositions logic) -



discrete mathematics - Prove or Disprove quantifiers (propositions logic) -

what approach can take solve these question: prove or disprove next statements. universe of discourse n = {1,2,3,4,...}.

(a) ∀x∃y,y = x·x (b) ∀y∃x,y = x·x (c) ∃y∀x,y = x·x.

the best way solve such problems first think them until you're confident can either proven or disproven.

if can disproven, have disprove statement provide counterexample. instance, b, can think of counterexample y=2. there no number x in n n*n = 2. thus, there counterexample, , statement false.

if statement appears true, may necessary utilize axioms or tautologies prove statment. instance, known 2 integers multiplied produce integer.

hopefully plenty of approach going.

logic discrete-mathematics quantifiers

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