4. In a commercial survey involving 1000 persons on brand preferences 120 prefer BRAND X only, 200 prefer BRAND Y only, 150 BRAND Z only, 370 prefer BRAND X or Y but not Z. 450 prefer BRAND Y or Z but...

Solve using the concept of counting techniques and application of venn diagram.

Extracted text: 4. In a commercial survey involving 1000 persons on brand preferences 120 prefer BRAND X only, 200 prefer BRAND Y only, 150 BRAND Z only, 370 prefer BRAND X or Y but not Z. 450 prefer BRAND Y or Z but not X. 370 prefer either BRAND Z or X but not Y and none prefer all the three. How many persons have no brand preferences?