3. Consider p(x) and g(x), where x U = {1,2}. If the following is true,...

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3. Consider p(x) and g(x), where x € U = {1,2}. If the following is true, give a rigorous argument. If it is false, give a counterexample. (Note that "p implies q" is the same as "if p, then q" and also as "p→q.") (i) (Vx = U, p(x) →q(x)) implies [ (Vx ≤ U, p(x)) → (Vx ≤ U, q(x)) ] ? What about its converse ? (ii) (3x = U, p(x) → q(x)) implies [ (3x € U, p(x)) → (3x € U, q(x)) ] ? What about its converse ? 3. Consider p(x) and g(x), where x € U = {1,2}. If the following is true, give a rigorous argument. If it is false, give a counterexample. (Note that "p implies q" is the same as "if p, then q" and also as "p→q.") (i) (Vx = U, p(x) →q(x)) implies [ (Vx ≤ U, p(x)) → (Vx ≤ U, q(x)) ] ? What about its converse ? (ii) (3x = U, p(x) → q(x)) implies [ (3x € U, p(x)) → (3x € U, q(x)) ] ? What about its converse ?

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Open sidebar i The statement xU pxqx implies xU px xU qx is true To prove this we need to show that ... View the full answer