Math Problem Solver

5. In a survey of 1000 households, 275 owned a home computer, 455 a video, 405 two cars, and

265 households owned neither a home computer, nor a video, nor two cars. Given that 145

households owned both a home computer and a video, 195 both a video and two cars, and 110

both two cars and a home computer. Find the number of households surveyed which owned;

i) a home computer, a video and two cars [3 marks]

ii) a video only [1 mark]

iii) two cars, a video but not a home computer [2 marks]

iv) a video, a home computer but not two cars [2 marks]

6. Construct the truth tables for the following statement formulas:

i) (𝑝 𝑞) ⟷ (𝑞 ⟶ 𝑟) [2 marks]

ii) (𝑝 ⟶ (𝑞 𝑟)) (¬ 𝑝)