Solution for Section 3.5 Question 3

3. When you are given a proposition such as  lfloor.jpg (691 bytes)x · yrfloor.jpg (530 bytes) = lfloor.jpg (691 bytes)xrfloor.jpg (530 bytes)· lfloor.jpg (691 bytes)yrfloor.jpg (530 bytes)and asked to determine if it is true or false, it is usually a good idea to try substituting some values for the variables x and y.

Let x = 3.9 and y = 2.8,  then

lfloor.jpg (691 bytes)x · yrfloor.jpg (530 bytes)lfloor.jpg (691 bytes)10.92rfloor.jpg (530 bytes)= 10

and

lfloor.jpg (691 bytes)xrfloor.jpg (530 bytes)· lfloor.jpg (691 bytes)yrfloor.jpg (530 bytes)= 3 · 2 = 6.

Thus the proposition  lfloor.jpg (691 bytes)x · yrfloor.jpg (530 bytes) = lfloor.jpg (691 bytes)xrfloor.jpg (530 bytes)· lfloor.jpg (691 bytes)yrfloor.jpg (530 bytes) is false.

Back to Section 3.5