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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To 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.
pay attention in class,,,, think it thin it , think different
The infinite set of numbers characterised by 468*k where k is an integer.
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.
18
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.
All multiples of 32, which is an infinite number.