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What is the DFA for the set of strings such that the number of 0s is divisible by 5 and the number of 1's divisible by 3?
Oh, what a happy little question! To create a DFA for this set of strings, we can think of states where the number of 0s and 1s seen so far are either divisible by 5 and 3, or not. By transitioning between these states based on the input symbols, we can paint a beautiful DFA that accepts strings with the desired properties. Just remember, there are no mistakes, only happy little accidents in the world of automata!
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JordanTo construct a Deterministic Finite Automaton (DFA) for the set of strings where the number of 0s is divisible by 5 and the number of 1s is divisible by 3, we would need to have states representing different remainders when divided by 5 and 3. The DFA would have 15 states, each corresponding to a pair of remainders (r1, r2) where r1 is the remainder when divided by 5 and r2 is the remainder when divided by 3. Transitions would be based on the input symbols 0 and 1, moving between states based on the remainders obtained after adding the current symbol's contribution. Accept states would be those where the remainders are both 0, indicating divisibility by 5 and 3.
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What are the number's divisible by 468?
The infinite set of numbers characterised by 468*k where k is an integer.
What numbers are 891 divisible by?
Every number is divisible by any non-zero number such as 891. Any element of the set of numbers of the form 891*k, where k is an integer, is evenly divisible.
If you take the 3 numbers in any consecutive trio and multiply them together to get a new number that new number will always be a multiple of 6 why is this?
18
What is the test for divisibility of 11?
Split the number into its alternate digits.Sum the digits in each setIf the difference between their sums is zero (0) or divisible by 11 then the original number is divisible by 11.ExamplesIs 1289324 divisible by 11?Split into alternate digits: 1_8_3_4 and _2_9_2 Sum each set of digits:1_8_3_4 -> 1+8+3+4 = 16_2_9_2 -> 2+9+2 = 13Difference between the sums: 16 - 13 = 3, not divisible by 11; so original number 1289324 is not divisible by 11.Is 19407278 divisible by 11?Split into alternate digits: 1_4_7_7 and _9_8_2_6 Sum each set of digits:1_4_7_7 -> 1+4+7+7 = 19_9_0_2_8 -> 9+0+2+8 = 19Difference between the sums: 19 - 19 = 0; so original number 19407278 is divisible by 11.
What number is divisible by 32?
All multiples of 32, which is an infinite number.
