Exercise B

Check all the claims made in introducing the new notational conventions in §10.3, i.e. show that:

1. ‘$((A\wedge B)\wedge C)$’ and ‘$(A\wedge(B\wedge C))$’ have the same truth table

2. ‘$((A\vee B)\vee C)$’ and ‘$(A\vee(B\vee C))$’ have the same truth table

3. ‘$((A\vee B)\wedge C)$’ and ‘$(A\vee(B\wedge C))$’ do not have the same truth table

4. ‘$((A\rightarrow B)\rightarrow C)$’ and ‘$(A\rightarrow(B\rightarrow C))$’ do not have the same truth table

Also, check whether:

1. ‘$((A\leftrightarrow B)\leftrightarrow C)$’ and ‘$(A\leftrightarrow(B\leftrightarrow C))$’ have the same truth table