# SOLUTION: Prove that: (a) P ) Q is not equivalent to Q ) P (b) P ) Q is not equivalent to :P ) :Q (c) P , Q , R is not equivalent to (P , Q) ^ (Q , R) Give shorter propositions which ar

Algebra ->  Algebra  -> Conjunction -> SOLUTION: Prove that: (a) P ) Q is not equivalent to Q ) P (b) P ) Q is not equivalent to :P ) :Q (c) P , Q , R is not equivalent to (P , Q) ^ (Q , R) Give shorter propositions which ar      Log On

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 Logic: Propositions, Conjunction, Disjunction, Implication Solvers Lessons Answers archive Quiz In Depth

 Click here to see ALL problems on Conjunction Question 521599: Prove that: (a) P ) Q is not equivalent to Q ) P (b) P ) Q is not equivalent to :P ) :Q (c) P , Q , R is not equivalent to (P , Q) ^ (Q , R) Give shorter propositions which are equivalent to: (a) T , T (b) T , F (c) P , T. (d) P , F. In a mathematics book we read y = x2 + 2x + 2 ) y = (x + 1)2 + 1 ) y >_ 1: that ist >_ littl equal Answer by solver91311(16897)   (Show Source): You can put this solution on YOUR website! Since is a concave up parabola such that the vertex is a minimum point and where the -coordinate of the vertex is equal to and the -coordinate of the vertex is , the minimum value of the function is, indeed, 1 and the given proposition is true. John My calculator said it, I believe it, that settles it