Truth Tables

Question 1

Truth Table for ‘And’ &

Answer 1

Question 2

Truth Table for ‘Or’ / ^

Answer 2

Question 3

Truth table for ‘Not’

Answer 3

Question 4

Truth table for If then

Answer 4

Question 5

Truth table for inclusive or

Answer 5

Question 6

Truth table for Exclusive or

Answer 6

Question 7

truth table for Iff

Answer 7

Question 8

Rules and steps for Complex truth tables

Answer 8

1. However many sentence letters are present in the sentence, we list them in alphabetical order on the left hand side of the table
2. The number of rows (ie. the number of different combinations of truth values) doubles for each sentence letter. We exhuast all combinations of Ts and Fs.
3. Next we fill in the columns under each sentence letter. Then we fill in the columns under any connectives, paying careful attention to the brackets to make sure we know which sentences they are connecting.
4. finally fill in the column under the main operator.

Question 9

what are Tautologies, contradiction and contingencies and their truth tables consist of?

Answer 9

Tautologies are truth-functionally true. This means their truth is guaranteed by the connectives. Their truth tables are all T’s.

Contradictions are truth-functionally false. This means their falsity is guarenteed by their connectives. Their truth tables are all F’s.

Contingencies are neither tautologies nor contradictions, so their truth tables are a mix of Ts and Fs.

(the main operators value is the one that is important)

Using this we can test for validity

Question 10

All the differnt logical operators and their symbols

Answer 10