Question

please determine of the statement is true or false
If x <3 and y <4 then xy <12
PLEASE ANSWER IT CORRECTLY

Answer 1

Answer:

true.

Step-by-step explanation:

keep in mind that, > means greater than and < means less than.

like that, if I say >12 then it means greater than 12 and <12 it means less than 12.

so, the question says if x is less than 3 and y is less than 4 then, is xy less than 12?

to solve that,

let's take x as 3 and y as 4.

that would mean xy = (3)x(4)

= 12

now, let's try greater numbers.

let's take x as 4 and y as 5

that would mean xy = (4)x(5)

= 20 is greater than 12 or simply, 20 = >12

finally, let's try lower numbers.

x = 2

y = 3

xy = (2)x(3)

= 6 is less than 12 or simply, 6 = <12

so numbers lower than 3 and 4 result in the product being lower than 12.

just like that, numbers greater than 3 and 4 result in the product being greater than 12.

so, true. if x <3 and y <4 then xy is of course, <12.

thanks.

Answer 2

The statement is true.

If x < 3 and y < 4, then the largest possible value of xy occurs when x = 3 and y = 4, giving xy = 12. Therefore, for any values of x and y that satisfy x < 3 and y < 4, we have xy < 12.

To prove it, we can use a direct approach.

Given that x < 3 and y < 4, we can multiply these two inequalities together to obtain:

xy < 34

Simplifying the right-hand side of the inequality, we get:

x*y < 12

Therefore, we have shown that if x < 3 and y < 4, then xy < 12. In other words, the statement is true.

Intuitively, the statement makes sense because if both x and y are less than 3 and 4 respectively, then their product must be less than the product of 3 and 4, which is 12.

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