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Consider the conjecture any number disciple by 2 is also divisible by 4 is each of the numbers 12 19 22 28 30 a counterexample of the conjecture ?

Number
12 19 22 28 30
Is the number a counterexample yes or no

1 answer

To determine if each of the numbers (12, 19, 22, 28, 30) is a counterexample to the conjecture "any number divisible by 2 is also divisible by 4," we need to check the divisibility of each number by 2 and then by 4.

  1. 12:

    • Divisible by 2: Yes (12 ÷ 2 = 6)
    • Divisible by 4: Yes (12 ÷ 4 = 3)
    • Counterexample: No

  2. 19:

    • Divisible by 2: No (19 is odd)
    • Counterexample: No (since it's not divisible by 2)

  3. 22:

    • Divisible by 2: Yes (22 ÷ 2 = 11)
    • Divisible by 4: No (22 ÷ 4 = 5.5)
    • Counterexample: Yes

  4. 28:

    • Divisible by 2: Yes (28 ÷ 2 = 14)
    • Divisible by 4: Yes (28 ÷ 4 = 7)
    • Counterexample: No

  5. 30:

    • Divisible by 2: Yes (30 ÷ 2 = 15)
    • Divisible by 4: No (30 ÷ 4 = 7.5)
    • Counterexample: Yes

To summarize:

  • 12: No
  • 19: No
  • 22: Yes
  • 28: No
  • 30: Yes

So, for your question, the numbers that are counterexamples to the conjecture are 22 and 30, and the others (12, 19, 28) are not counterexamples.