The universe of discourse for both P (x) and Q (x) is all UNL students. Express the statement \Every computer science student must take a discrete mathematics course". 8x(Q (x) ! P (x)) Express the statement \Everybody must take a discrete mathematics course or be a computer science student". 8x(Q (x) _ P (x)) Are these statements true or false ... in which · signifies “and” and ⊃ signifies “if . . . then.” (In the “or” table, for example, the second line reads, “If p is true and q is false, then p ∨ q is true.”) Truth tables of much greater complexity, those with a number of truth-functions, can be constructed by means of a computer. The statement A ⊕ B is true when either A or B, but not both, are true. A ⊻ B means the same. (¬ A ) ⊕ A is always true, and A ⊕ A always false, if vacuous truth is excluded.

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if q is false, then q->~r is true, whether or not ~r is true. the only time q->~r is false is if q is true and ~r is false. this is your truth table for the implied statement. Definition: A conditional statement, symbolized by p q, is an if-then statement in which p is a hypothesis and q is a conclusion. The logical connector in a conditional statement is denoted by the symbol . The conditional is defined to be true unless a true hypothesis leads to a false conclusion. A truth table for p q is shown below. p, so that (1¡‚) ˘ 1 q. The desired result is trivial if u ˘0 or v ˘0, so assume they are both strictly positive. Letting x ˘logup and y ˘logvq, the above inequality becomes e 1 p logu p¯1 q logv q • 1 p e logup ¯ 1 q e logv elogu¯logv • up p ¯ vq q uv • u p p ¯ vq q. (b)By part (a), for every x 2[a,b] we have f (x)g(x ...

If p, then q, where p and q are sentences, is. If q, then p. Clearly, if an If-then sentence is true, its converse is not necessarily true. Problem 9. State the converse of each statement, and then decide whether the converse is true. (Note that each statement is true.) a) If a number ends in 5, then it is a multiple of 5. The value of p will always true because if the value of p is false there is no chance that p-->q would result in true. The answer will be different if q=false because in this case p=false still giving true result. punineep and 107 more users found this answer helpful 4.3Summary. If we are proving p → q, then A direct proof begins by assuming p is true. : : until we conclude q. An indirect proof begins by assuming ~q is true. : : until we conclude ~p . An example of a proof by contradiction. Example 7: Prove that 2 is irrational. Proof: Assume by way of contradiction that can be represented as a quotient of two integers p/q with q ≠ 0.

Nuestro equipo tiene como misión, trabajar a la par con usted en las metas y objetivos que se ha propuesto, de manera que podamos lograr su completa satisfacción en los servicios que le proveemos p q p / q Let p = ‘It will rain’ and let q = ‘Jones will bring an umbrella.’ The following argument will be valid: If it will rain then Jones will bring an umbrella. It will rain. So, Jones will bring an umbrella. If these premises are true, then this conclusion must be true, too. Again, notice that you do not have to Third, let us continue with P and Q as above. The sentence ``if [P and Not(P)], then Q'' is always true, regardless of the truth values of P and Q. This is the principle that, from a contradiction, anything (and everything) follows as a logical conclusion. The table below explores the four possible cases, but the truth is simpler than that.