For all numbers a and b, let be defined by . For all numbers x, y, and z, which of the following must be true? I. II. III. A. I onlyB. II onlyC. III onlyD. I and II onlyE. I, II, and III
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Originally Posted by aeroflix For all numbers a and b, let be defined by . For all numbers x, y, and z, which of the following must be true? I. II. III. A. I onlyB. II onlyC. III onlyD. I and II onlyE. I, II, and III you just have to convert each side of the equation to see if it's true ... $\displaystyle x \odot y = xy + x + y$ $\displaystyle y\odot x = yx + y + x$ since $\displaystyle xy+x+y = yx+y+x$ for all real numbers, statement I is true. now check the other two ...
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