Truth Table Help?

Question

Fill the headings of the following truth table using p, q, ~, -->, v, and ^.

Heres the Table So Far.
I have to fill in the headings of columns a and b
using those symbols above. Help please :o)

P Q (a) (b)
----------------
T T T F
T F T F
F T T F
F F F T

Answer 1

I don't recognize your symbols, but I remember truth tables so here goes.

(a) will be P or Q

(b) will be P' and Q'

Answer 2

p q (-q ^ p) -> ~q T T T F F T F F One key component to be sure about conditionals is they are pretend in user-friendly words in a unmarried case: T --> F. In all different circumstances, the conditional is authentic. For conditionals, word that once the ensuing is authentic, the finished conditional is authentic. intending to verify that ~q to be authentic, q must be pretend. For both cases q is pretend, the conditional will be authentic. p q (-q ^ p) -> ~q T T T F . . . . . T . . . . . . F T F F . . . . . T . . . . . . For the different 2 circumstances, all we ought to do is plug contained in the boolean values. If p = T and q = T, then we've (~q ^ p) --> ~q (~T ^ T) --> (~T) (F ^ T) --> F F --> F, that is a real actuality. p q (-q ^ p) -> ~q T T . . . . . T . . . . . . T F . . . . . T . . . . . . F T F F . . . . . T . . . . . . Now, evaluate the case the position p = F and q = T. Then (~q ^ p) --> ~q (~T ^ F) --> ~T (F ^ F) --> F F --> F, that is a real actuality. for this reason: p q (-q ^ p) -> ~q T T . . . . . T . . . . . . T F . . . . . T . . . . . . F T . . . . . T . . . . . . F F . . . . . T . . . . . .

Answer 3

column a is p v q
since it is true when either p or q is true

column b is ~p ^ ~q
since the column only comes up true if ~p and ~q both are true (in this case if p and q are both false)

Answer 4

a) If p or q = T, then a = T; otherwise a = F
b) If p and q = F, then b = T; otherwise b = F

Sorry, don't understand your notation; so here's the logic in a sort of pseudocode.

Answer 5

Good question

a)
p v q


b)
~p ^ ~q