Question

SYMBOLIC LOGIC QUESTION-

Translate the following sentences into symbolic logic notation.

1.Unless c is to the right of a, it is small.

2. a is large if and only if it’s a cube that is to the left of b.

3. a is to the left or right of d if it’s not a cube.

4. If b and d are cubes, then either a or c is a tetrahedron.

5. e is a tetrahedron if and only if it is neither a cube nor a dodec.

Answer 1

1. Let p = C is to the right of a

and q = c is small

" c is big if and only if it is to the right of a"

i.e.   

2. Let p = a is large

and q = a is a cube

and r = a is to the left of b

"a is large if and only if it’s a cube and it is to the left of b"

3. Let p = a is to the left of d

q = a is to the right of d

r = a is a cube

"a is to the left or right of d if it’s not a cube"

4. Let p = b is a cube

q = d is a cube

r = a is a tetrahedron

s = c is a tetrahedron

"If b and d are cubes, then either a or c is a tetrahedron."

5.

Let p = e be a cube

q = e be a dodec

r = e be a tetrahedron

e is a tetrahedron if and only if it is neither a cube nor a dodec