Existential Statements

An existential statement is a statement that announces the existence of a fact. To indicate an existential statement we use the words there is or there are or there exists. Some of the examples are:

  • There is a number n such that n*n=441
  • There exists 2 consecutive prime numbers

Let us solve some sums based on this.

  1. Express the statement 1234546789 is a multiple of 3 as an existential statement. Is it true?

To express any statement as an existential we use the words there is or there are or there exists. So the above statement can be expressed as:

There is a natural number x such that 123456789=3x.

By division process, we see that 123456789=3*41152263. So the statement is true.

2. What is the connection between the facts 3*3+4*4=5*5, 5*5+12*12=13*13, 7*7+24*24=25*25 and the statement there are numbers a,b,c such that a*a+b*b=c*c?

By solving the above equations, we see that 3*3+4*4=5*5, 5*5+12*12=13*13 and 7*7+24*24=25*25.

So, we can conclude that the facts are examples of the statement and the statement a*a+b*b=c*c stands true.

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