Question

Which of the following sequences of symbols are well-formed formulas (wffs)?

Put an ‘x’ or a ‘√’ after each sequence. Or put ‘yes’ or ‘no’ after each sequence.

1. Z ☺ B

2. C v ~ C v

3. ~ A * ~ ~ B

4. ~ ( Z --> Z)

5. (A --> B) --> (C ≡ D) --> (E v F --> G)

6. A --> (E D )

7. ~A --> (A v ~ A)

8. ~~A --> (A v A)

9. Z v BB

10. ~Z v ~BB

Answer 1

Solution for question is provided below. If any doubt please comment it below.

Well formed formulas are the expressions that satisfy the syntactic rules of propositional logic. The given expressions and their validity is provided below.

1. Z ☺ B	No	Not a valid operator
2. C v ~ C v	No	v should have two inputs
3. ~ A * ~ ~ B	No	Parenthesis should be there for * operator
4. ~ ( Z --> Z)	Yes
5. (A --> B) --> (C ≡ D) --> (E v F --> G)	No	(E v F --> G) is not a well formed formula
6. A --> (E D )	No	No binary operator between E and D
7. ~A --> (A v ~ A)	Yes
8. ~~A --> (A v A)	Yes
9. Z v BB	No	No parenthesis for operator v
10. ~Z v ~BB	No	No parenthesis for operator v