Thus the statement ‘If I am the king of England, the moon is made of blue cheese’ is ‘true’ (assuming I am not the king of England), and so is the statement ‘If I am the king of England, the moon is NOT made of blue cheese’. Thus, ‘B’ AND ‘not B’.
This doesn’t prove B and not B, it proves (~A OR B) AND (~A OR ~B), which is true since A is false (you are not the King of England).
This doesn’t prove B and not B, it proves (~A OR B) AND (~A OR ~B), which is true since A is false (you are not the King of England).