- #1
Ed Quanta
- 297
- 0
If E has m elements and F has n elements, how many elements does E x F have?
My thinking is that E x F would either have m or n elements. If m= n, then E x F would have m elements (or n elements). If m>n, then E x F would have n elements since E x F ={(x,y): x is an element of E and y is an element of F}. This of E has more elements than F, then there could only be n (x,y) pairs since there would only be n y's.Am I correct?
Also, if E x F is an empty set, then it would follow that E or F would have to be an empty set,right?
My thinking is that E x F would either have m or n elements. If m= n, then E x F would have m elements (or n elements). If m>n, then E x F would have n elements since E x F ={(x,y): x is an element of E and y is an element of F}. This of E has more elements than F, then there could only be n (x,y) pairs since there would only be n y's.Am I correct?
Also, if E x F is an empty set, then it would follow that E or F would have to be an empty set,right?