How do I solve this in a truth table?

Question

I am unsure if this is the right place to put this, but I am stuck... We define two new operations $\bar ∨$ and $\bar ∧$, defined by $$ a\bar ∨b = ¬(a ∨ b)\\ a\bar ∧b = ¬(a ∧ b) $$

2.a) Give the truth table for the operations $\bar ∨$ and $\bar ∧$.

The thing I need help with is what the symbols mean with a truth table, and what they do. Sorry for being unclear. Thanks for the help :D

Answer 1

To create the Truth table of an operation, just substitute and estimate the statement to get the result.

for $a\bar{\wedge} b$ you get for example:

• $T \bar{\wedge} T = ¬(T ∧ T) = ¬(T) = F $
• $T \bar{\wedge} F = ¬(T ∧ F) = ¬(F) = T $
• $F \bar{\wedge} T = ¬(F ∧ T) = ¬(F) = T $
• $F \bar{\wedge} F = ¬(F ∧ F) = ¬(F) = T $

Answer 2

For the first operation you get truth table:

$\begin{matrix} a& b & a\lor b & \lnot (a \lor b)\\ T & T &T & F\\ T & F & T & F\\ F & T & T & F \\ F & F & F & T \end{matrix}$

and for the second operation you get:

$\begin{matrix} a& b & a\land b & \lnot (a \land b)\\ T & T &T & F\\ T & F & F & T\\ F & T & F & T\\ F & F & F & T \end{matrix}$