GO Classes Weekly Quiz 2 | Programming in C | Propositional Logic | Question: 5

Answer 1

Every proposition is either true or false, but not both. So, for each propositional variable, we have two choices.
A truth table will need $2^n$ rows if there are $n$ propositional variables.
Since, we have $4$ propositions $p,r,q,t;$ So, $2^4 =16$ rows in truth table.

Answer 2

In this compound proposition, there are four different propositional variables{p,q,r,t}. Each propositional variable has two choices: “True” or “False”.

if we have n different proposition variables and each of them has 2 choices so the number of rows will be $2^{n^{}}$, where 2 represents two choices “true” or “false” and n represent a number of variables.

now in question, it is given 4 different propositional variables so,

                        number of rows = $2^{4^{}}$

                                                = 16

hence, there are 16 rows in the truth table of the given compound proposition.

Answer 3

Since there are 4 inputs. So no of combinaton is 4^2 = 16 as each input can be either true or false.

Comments

the wrong concept is being used let’s say you have 5 inputs then according to your concept 5^2 = 25 rows in the truth table but actually, it will be 2^5 =32 rows in the truth table.

Answer 4

We know that for answering any proposition there is only two choice(either True or False). As the above compound proposition uses only 4 propositional variable

so, its models will be  2^4 = 16 (0 to 15th row).