Question

The following grammar generates the logical expressions. The symbols and, or, not refer to the familiar concepts in logic: conjunction, disjunction and negation. Which one of these operators has the highest precedence in this grammar?

. s = c
c = c and d | d
d = a | a or d
a = not a | 0 | 1

Answer 1

In the grammar provided, the 'not' operator has the highest precedence, followed by 'and', and then 'or' having the lowest precedence.

Step-by-step explanation:

The grammar presented for generating logical expressions indicates that the negation operator has the highest precedence. This is because in the rule 'a = not a | 0 | 1', the negation operator not is applied directly to the atom 'a' before any other logical operators are considered. In comparison, the 'and' operator comes next in precedence, as shown in the rule 'c = c and d | d', where 'and' is used to combine c and d before using the disjunction operator 'or', which has the lowest precedence as illustrated by the rule 'd = a | a or d'. The highest precedence operator is the one closest to the atom, which in this case is 'not'.

Answer 2

In this grammar, the operator with the highest precedence is the negation operator 'not'. Option D

In the provided grammar for logical expressions, the highest precedence operator is the negation operator "not".

The grammar rules indicate that the symbol 'a' can be a logical expression containing 'not a'.

As per the grammar, 'not' is applied directly to 'a', '0', or '1'. This implies that the negation operation has the highest precedence because it directly operates on the atomic propositions 'a', '0', or '1', altering their truth values before other logical operations like 'and', 'or' are performed.