###### GATE 2022

August 11, 2023###### GATE 2004-IT

August 12, 2023# TIFR PHD 2022

Question 3 |

A binary string is a sequence of 0’s and 1’s. A binary string is finite if the sequence is finite, otherwise it is infinite. Examples of finite binary strings include 00010100, and 1111101010. Which of the following is TRUE about the set of all finite binary strings and the set of all infinite binary strings?

The set of all finite binary strings is countable while the set of all infinite binary strings is uncountable | |

The set of all finite binary strings is uncountable while the set of all infinite binary strings is countable | |

The set of all finite binary strings and the set of all infinite binary strings are both countable | |

The set of all finite binary strings and the set of all infinite binary strings are both uncountable | |

The set of all finite binary strings is countable while whether the set of all infinite binary strings is countable or not is not known |

Correct Answer: A

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