Question

1+4=5 2+5=12 3+6=21 8+11=? can anyone solve this? ​

Answer 1

Explanation:

the digit symbols and the operators + and = are being used in their conventional mathematical senses, then the answer can be anything you wish. This is because a statement of the form “if something-false then something” is always true in a mathematical logical sense. For example, “if 2+5=12 then I am Donald Trump” is a true statement, and remains true whatever you put in the second half, because 2+5 does not equal 12 with the symbols and operators being used in their conventional senses. So I could say “if 1+4=5 , 2+5=12 , and 3+6=21 , then 8+11=3.14159265 ”, and nobody can gainsay this claim: it’s as true as any other similar statement.

However, if we suppose that either the digit symbols or the operators are being used other than in their conventional senses, there are many and varied ways we can think of that happening. Some are more useful than others. For example, if we simply suppose that the symbol = is being used to denote ≠ , that makes the three premiss statements true but tells us nothing that helps us answer the final question: any value other than 19 becomes a possible answer.

One natural way to consider that symbols or operators are being used other than in their conventional senses is to suppose that the digits and the equality sign have their usual meanings but the operator + is being used in a non-standard way. For clarity, let us replace it with an alternative symbol, for example ⊕ .

One example:

Define ⊕:N×N→N s.t. (n,m)↦n(m+1)

Then 1⊕4=1×(4+1)=1×5=5 , 2⊕5=2×6=12 , 3⊕6=3×7=21 , and 8⊕11=8×12=96

But there are infinitely many different definitions we could come up with that would work equally well. Indeed, we could contrive any particular answer we wish for.

Another example:

Define ⊕:N×N→Q s.t. (n,m)↦1524nm+314−1336n2m2

Then 1⊕4=(1524⋅1⋅4)+314−(1336⋅12⋅22)=456+314−121=5 , 2⊕5=12 , 3⊕6=21 , and 8⊕11=833

Answer 2

Answer:

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Explanation:

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