is (((a and b) and c) and d) equal to a and b and c without parentheses?
Why?
If you mean, $\Big(\big((a\wedge b)\wedge c\big)\wedge d\Big) ~=~ a\wedge b\wedge c\wedge d$ , then this is indeed true due to the associative property of logical conjunction.
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If you mean, $\Big(\big((a\wedge b)\wedge c\big)\wedge d\Big) ~=~ a\wedge b\wedge c\wedge d$ , then this is indeed true due to the associative property of logical conjunction.