Question

Let p = {1, 3, 5, 7} , q = {3, 7, 9, 11} , r = {1, 5, 8, 11} then verify the following
1: p U q = q U p
2: ( p U q ) U r = p U (q U r )
3: p ∩ ( q ∪ r ) = ( p ∩ q ) U ( p ∩ r )
hope so anyone will answer me :)

Answer 1

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$p \: u \: q \: = q \: u \: p \\ p = 1 \: 3 \: 5 \: 7 \\ q = 3 \: 7 \: 9 \: 11 \\ r = 1 \: 5 \: 8 \: 11 \\ p \: u \: q \: = 3 \: 7 \\ q \: u \: p \: = 3 \: 7 \\ so \: p \: u \: q \: = \: q \: u \: p \\ \\ \\ \\ \\ \\ \\ \\ p \: u \: q \: u \: r = p \: u \: q \: r \\ p \: u \: q = 3 \: 7 \\ q \: u \: r \: = 11 \\ 3 \: 7 \: u \: 1 \: 5 \: 8 \: 11 = 1 \: 3 \: 5 \: 7 \: u \: 11 \\ there \: is \: no \: union \: on \: both \: sides \: so \: they \: are \: equal \\ \\ \\ \\ \\ \\ \\ \\ \\ 1 \: 3 \: 5 \: 7 \: n \: 11 = 1 \: 3 \: 5 \: 7 \: 9 \: 11 \: u \: 1 \: 3 \: 5 \: 7 \: 8 \: 11 \\ 1 \: 3 \: 5 \: 7 \: 11 = 1 \: 3 \: 5 \: 7 \: 11$