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There are lot of ways to use grep with logical operators.

1. Use \| to separate multiple patterns for the OR condition.

   Example: grep 'pattern1\|pattern2' filename

2. Use the -E option to send multiple patterns for the OR condition.

   Example: grep -E 'pattern1|pattern2' filename

3. Using a single -e matches only one pattern, but using multiple -e option matches more than one pattern.

   Example: grep -e pattern1 -e pattern2 filename

4. grep -v can simulate the NOT operation.

5. There is no AND operator in grep, but you can brute-force simulate AND by using the -E option.

   Example : grep -E 'pattern1.*pattern2|pattern2.*pattern1' filename

   The above example will match all the lines that contain both pattern1 and pattern2 in either order.)