Exercises

Monday, 18 February 2019

10:43 AM

$𝑙𝑒𝑡 𝐴=﷐𝑎,﷐𝑎﷯﷯ What are the elements of 𝐴 - 𝑎 and {𝑎} What is ﷐𝐴﷯ - 2 --- ℕ⊂ℤ⊂ℚ⊂ℝ⊂ℂ --- 𝑙𝑒𝑡 𝑆=﷐𝑎,𝑏,𝑐﷯ (?) ﷐𝑎﷯ ﷐𝑏﷯ ﷐𝑐﷯ ﷐𝑎,𝑏﷯ ﷐𝑎,𝑐﷯ ﷐𝑏,𝑐﷯ ﷐𝑎,𝑏,𝑐﷯ The subsets of 𝑆 are: --- 𝑙𝑒𝑡 𝐴={0,1,﷐0,1﷯} What are the elements of 𝐴 - 0, 1, ﷐0,1﷯ ﷐?﷯ ﷐0﷯ ﷐1﷯ ﷐﷐0,1﷯﷯ ﷐0,1﷯ ﷐0,﷐0,1﷯﷯ ﷐1,﷐0,1﷯﷯ ﷐0,1,﷐0,1﷯﷯ What are the subsets of 𝐴: What is 𝑃(𝐴) = ^ all of that .. What is |𝑃﷐𝐴﷯| - ﷐2﷮3﷯=8 Is ﷐?﷯∈𝐴 - No Is ﷐?﷯⊂𝐴 - Yes Is (?)∈𝑃(𝐴) - Yes Is ﷐?﷯⊂𝑃(𝐴) - Yes Is 0∈𝐴 - Yes Is 0⊂𝐴 - No Is ﷐0,1﷯∈𝐴 - Yes Is ﷐0,1﷯∈𝑃(𝐴) - Yes Is {﷐0,1﷯} ?????? - No Is {﷐0,1﷯} ?????? - Yes --- 𝑙𝑒𝑡 𝑈=﷐1,2,3,4,5,6﷯ 𝑙𝑒𝑡 𝐴=﷐1,3,5﷯ 𝑙𝑒𝑡 𝐵=﷐1,2﷯ ﷐𝐴﷮𝑐﷯=﷐2,4,6﷯$
$﷐𝐴﷮𝑐﷯=﷐2,4,6﷯ 𝐴\intersectionB=﷐1﷯ 𝐴\unionB=﷐1,2,3,5﷯ 𝐴−𝐵=﷐3,5﷯ --- 𝑙𝑒𝑡 𝑈=﷐0,1,2,3,4,5,6,7,8,9﷯ 𝐴=﷐𝑥∈𝑈﷮𝑥 𝑖𝑠 𝑜𝑑𝑑﷯ - {1,3,5,7,9} 𝐵=﷐𝑥∈𝑈﷮𝑥 𝑖𝑠 𝑒𝑣𝑒𝑛﷯ - {0,2,4,6,8} 𝐶=﷐𝑥∈𝑈﷮𝑥 𝑖𝑠 𝑎 𝑚𝑢𝑙𝑡𝑖𝑝𝑙𝑒 𝑜𝑓 3﷯ - {0,3,6,9} 𝐷=﷐𝑥∈𝑈﷮𝑥 𝑖𝑠 𝑝𝑟𝑖𝑚𝑒﷯ - ﷐2,3,5,7﷯ 𝐴\𝑖𝑛𝑡𝑒𝑟𝑠𝑒𝑐𝑡𝑖𝑜𝑛𝐶=﷐3,9﷯ 𝐵−𝐷=﷐0,4,6,8﷯ 𝐵\unionD=﷐0,2,3,4,5,6,7,8﷯ ﷐𝐷﷮𝑐﷯=﷐0,1,4,6,8,9﷯ 𝐴\intersectionC−𝐷=﷐9﷯ --- 𝐷𝑒𝑡𝑒𝑟𝑚𝑖𝑛𝑒 𝑡ℎ𝑒 𝑠𝑒𝑡𝑠 𝐴 𝑎𝑛𝑑 𝐵 𝑤ℎ𝑒𝑟𝑒 * 𝐴−𝐵=﷐𝑎,𝑐﷯ * 𝐵−𝐴={𝑏,𝑓,𝑔} * 𝐴\intersectionB={𝑑,𝑒} 𝐴=﷐𝑎,𝑐,𝑑,𝑒﷯ 𝐵={𝑏,𝑑,𝑒,𝑓,𝑔} --- ﷐𝐴﷯=112 ﷐𝐵﷯=89 ﷐𝐶﷯=71 ﷐𝐴\intersectionB﷯=32 ﷐𝐴\intersectionC﷯=26 ﷐𝐵\intersectionC﷯=43 ﷐𝐴\intersectionB\intersectionC﷯=20 Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings $