Practice 21, p. 47

Prove:

Exercise #11, p. 57

Prove:

Exercise #3, p. 56

Find an interpretation to prove that this wff is not valid:

and find the flaw in the ``proof'' given.

Let x and y have domain the reals, and Q(x,y) be the condition that . Then the antecedent above says that for every real y, there is another real x such that - every real has a square in the real numbers. However, the consequent says that there is a real number x which is the square of all reals! False.

Find the flaw in the ``proof'':

In step 4, the student attempted universal generalization from step 3, which was deduced by existential instantiation of step 2, in which y was free.

Practice 24, p. 47

Prove: