 Hello and welcome to the session in this session. We will discuss the following question and the question says state the cardinal number of the following sets Part one a is equal to letters of the word block Part two colors of a rainbow Part three n is equal to once having 35 days Part four set a is equal to the set containing the words French Spanish Japanese English Part five p is equal to the set containing x such that x is equal to n cube Where n belongs to n that is the set of natural numbers n is less than equal to 5 Before we start solving the question, let us see what is cardinal number of a set cardinal number Off a set a is the number of Distinct elements of the set and it is denoted by m of a This is a key idea for this question and using this key idea. We will solve the question Let's start the solution now In part one, we are given set a is equal to letters of the word clock so in part one we have a is equal to letters of the word block Now we have to find the cardinal number of the set a and using the key idea We have cardinal number of the set a is the number of distinct elements of the set Now the distinct letters of the word clock are c l o K so the set a can be written in this to form as the set containing the elements C whole o K We can see that the set a contains four elements So the number of elements of the set a is four Therefore the cardinal number of a that is L of a is equal to four So this is your answer for part one. We will now move on to part two In part two, we have colors of the rainbow We know that there are Seven colors in a rainbow So there are seven elements in the given set therefore The cardinal number of the set is equal to seven This is your answer for part two Now in part three we have m is equal to months having thirty five days So for part three m is equal to months having thirty five days Now we know that there is no such month having thirty five days therefore The set a has no elements This implies the cardinal number of m that is is equal to zero This completes our part three We now move on to part four Part four is set a is equal to the set containing the words French Spanish Japanese English We can see that set a contains four words So the number of elements of the set a is equal to four Therefore the cardinal number of a that is L of a is equal to four This is your answer for part four We now move on to part five In part five he is equal to this set That is p is equal to the set containing x such that x is equal to n cube where n belongs to n, which is the set of natural numbers and m is less than equal to five So set p contains the cubes of all natural numbers which are less than equal to five We will now write down the elements of the set p The elements the set p One cube which is equal to one Two cube which is equal to eight Three cube which is equal to twenty seven third cube which is equal to sixty four and Five cube which is equal to 125 Let's now write down set p in rest of form So the set p is Equal to the set containing the elements one eight Twenty seven sixty four one twenty five You can see that the set p contains five elements the number of elements of the set p is Equal to five Therefore the cardinal number of the set p that is n of p is equal to five This is our answer for part five With this we end our session. Hope you enjoyed the session