Question

In: Statistics and Probability

1. Show that the argument (a) p → q       q → p       therefore p...

1. Show that the argument

(a) p → q

      q → p

      therefore p V q

      is invalid using the truth table. ( 6 marks )

(b) p → q

      P

      therefore p

       is invalid using the truth table. ( 6 marks )

(c) p → q

      q → r

       therefore p → r

        is invalid using the truth table. ( 8 marks )

Solutions

Expert Solution

We will construct the truth table for this:


Related Solutions

Is the following argument p& ∼ p,(p ∨ q) ≡ (s ≡ (t ∨ p)) ∴...
Is the following argument p& ∼ p,(p ∨ q) ≡ (s ≡ (t ∨ p)) ∴ r valid? If not provide a counterexample.
Let p and q be propositions. (i) Show (p →q) ≡ (p ∧ ¬q) →F (ii.)...
Let p and q be propositions. (i) Show (p →q) ≡ (p ∧ ¬q) →F (ii.) Why does this equivalency allow us to use the proof by contradiction technique?
Show that if P;Q are projections such that R(P) = R(Q) and N(P) = N(Q), then...
Show that if P;Q are projections such that R(P) = R(Q) and N(P) = N(Q), then P = Q.
Using logical equivalence laws, show that (((p v ~ q) ⊕ p) v ~p) ⊕ (p...
Using logical equivalence laws, show that (((p v ~ q) ⊕ p) v ~p) ⊕ (p v ~q) is equivalent to p v q. v = or, ~ = not, ⊕ = exclusive or (XOR). Please show the steps with the name of the law beside each step, thanks so much!
Let q and p be natural numbers, and show that the metric on Rq+p is equivalent...
Let q and p be natural numbers, and show that the metric on Rq+p is equivalent to the metric it has if we identify Rq+p with Rq × Rp.
(c) (¬p ∨ q) → (p ∧ q) and p (d) (p → q) ∨ p...
(c) (¬p ∨ q) → (p ∧ q) and p (d) (p → q) ∨ p and T I was wondering if I could get help proving these expressions are logically equivalent by applying laws of logic. Also these 2 last questions im having trouble with. Rewrite the negation of each of the following logical expressions so that all negations immediately precede predicates. (a) ¬∀x(¬P(x) → Q(x)) (b) ¬∃x(P(x) → ¬Q(x))
Using a truth table determine whether the argument form is valid or invalid p ∧ q...
Using a truth table determine whether the argument form is valid or invalid p ∧ q →∼ r p∨∼q ∼q→p ∴∼ r
1. Suppose that the market demand is described by P = A – B(Q+q) where P...
1. Suppose that the market demand is described by P = A – B(Q+q) where P is the market price, Q is the output of the incumbent firm, and q is the output of the potential entrant to the market. The incumbent’s total cost function is C(Q) = c1Q, whereas the cost function of the entrant is C(q) = c2q+F. a. If the entrant firm observes the incumbent producing Q* units of output and expects this output level to be...
1.) Suppose that the statement form ((p ∧ ∼ q)∨(p ∧ ∼ r))∧(∼ p ∨ ∼...
1.) Suppose that the statement form ((p ∧ ∼ q)∨(p ∧ ∼ r))∧(∼ p ∨ ∼ s) is true. What can you conclude about the truth values of the variables p, q, r and s? Explain your reasoning 2.Use the Laws of Logical Equivalence (provided in class and in the textbook page 35 of edition 4 and page 49 of edition 5) to show that: ((∼ (p ∨ ∼ q) ∨ (∼ p ∧ ∼ r)) ∧ s) ≡ ((r...
For p, q ∈ S^1, the unit circle in the plane, let d_a(p, q) = min{|angle(p)...
For p, q ∈ S^1, the unit circle in the plane, let d_a(p, q) = min{|angle(p) − angle(q)| , 2π − |angle(p) − angle(q)|} where angle(z) ∈ [0, 2π) refers to the angle that z makes with the positive x-axis. Use your geometric talent to prove that d_a is a metric on S^1.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT