Define the binary operator by: ab=a² + b² and by: a b = 8a+ 8b Find the following. When simplifying, use the order of operations, that is, do the parentheses first. (52) + 7 =
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- Define the binary operator ⋄⋄ by: a⋄b=7a+7b and □ by: a□b=a2+b2 Find the following. When simplifying, use the order of operations, that is, do the parentheses first. (4 ⋄ 5)□ 2=Define the binary operator @ by: aa@b=2bb=2b and □□ by: a□b=a2+b2a□b=a2+b2 Find the following. When simplifying, use the order of operations, that is, do the parentheses first. (3(3 @ 8)8) □□ 7=7=Define the binary operator # by: aa#b=b=the smaller value of aa or bb and ∇∇ by: a∇b=7a∇b=7 Find the following. When simplifying, use the order of operations, that is, do the parentheses first. (6(6 # 3)3) ∇∇ 4=4=
- Define the binary operator :) by: aa :)b=7a+2b+8b=7a+2b+8 and ⋆⋆ by: a⋆b=a+6ba⋆b=a+6b Find the following. When simplifying, use the order of operations, that is, do the parentheses first. (5(5 :) 3)3) ⋆⋆ 4=4=Define the binary operator ⊗⊗ by: a⊗b=a2+b+3a⊗b=a2+b+3 Simplify each of the following. Do the order of operations (do what is in parentheses first). (3⊗6)⊗5=(3⊗6)⊗5= (7⊗4)⊗2=(7⊗4)⊗2=Define the binary operator ⊗⊗ by: a⊗b=a2+b+4a⊗b=a2+b+4 Find each of the following: 2⊗3=2⊗3= 8⊗8=8⊗8= 3⊗2=3⊗2= y⊗i
- Define the binary operator # by: aa#b=b= the smaller value of aa or bb.; Find each of the following: 44#2=2= 88#8=8= 22#4=4=Define the binary operator # by: aa#b=b= the smaller value of aa or bb.; Simplify each of the following. Do the order of operations (do what is in parentheses first). (5(5#9)9) # 8=8= (7(7#6)6) # 3=Define the binary operator ⋆ by: a ⋆ b = a + 4 b Simplify each of the following. Do the order of operations (do what is in parentheses first). a) ( 6 ⋆ 7 ) ⋆ 4 = b) ( 2 ⋆ 5 ) ⋆ 3 = Step by step, please
- Define the binary operator @ by: aa@b=2bb=2b Find each of the following: 77@5=5= 44@4=4= 55@7=7= mm@u=u=Define the binary operator ⊗⊗ by: a⊗b=a2+b+5a⊗b=a2+b+5 Find each of the following: 7⊗4=7⊗4= 2⊗2=2⊗2= 4⊗7=4⊗7= s⊗r=s⊗r=Define an operation ∗ on Z+ as follows: For a,b ∈ Z+, a∗b = a−b+1. Show that ∗ is a binary operation on Z. What is 3 ∗ 5? Is ∗ commutative? Is (2 ∗ 3) ∗ 4 = 2∗(3∗4)? Can you conclude that is ∗ associative