Of the integers between 1 and 700 (inclusive), 350 of them are even:
[tex]\left\lfloor\dfrac{700}2\right\rfloor=\lfloor350\rfloor=350[/tex]
100 of them are exact multiples of 7:
[tex]\left\lfloor\dfrac{700}7\right\rfloor=\lfloor100\rfloor=100[/tex]
Half of these are multiples of 14:
[tex]\left\lfloor\dfrac{700}{14}\right\rfloor=\lfloor50\rfloor=50[/tex]
This means the number of distinct integers in the given set that are multiples of 2 or 7 is
[tex]350+100-50=400[/tex]
