GATE CSE 2024 Session 1 Q61: Strings of length ≤ 5 in neither 0* + 1* nor 01* + 10*

Consider the following two regular expressions over the alphabet $\{0, 1\}$ :

$r = 0^* + 1^*$ $s = 01^* + 10^*$

The total number of strings of length less than or equal to 5, which are neither in $r$ nor in $s$ , is _________

Try it: numerical answer: type the value

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Numerical answer. No negative marking.

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Answer: 44 (official GATE 2024 final answer key)

Concept used: Complement counting with inclusion–exclusion.

First step: There are $2^6 - 1 = 63$ strings of length 0 to 5; count those in $r$ , in $s$ , and in both.

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Source: official GATE 2024 Session 1 CS question paper and final answer key, organised by IISc Bangalore. Question paper · Answer key