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Define the binary operator □□ by:
a□b=a3+b3a□b=a3+b3
Find each of the following:
- 4□5=4□5=
- 3□3=3□3=
- 5□4=5□4=
- z□g=z□g=
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- Define the binary operator ∇∇ by: a∇b=9a∇b=9 Find each of the following: 3∇5=3∇5= 8∇8=8∇8= 5∇3=5∇3= v∇n=v∇n=Define the binary operator □□ by: a□b=a3+b3a□b=a3+b3 Find each of the following: 2□4=2□4= 5□5=5□5= 4□2=4□2= p□c=p□c=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: 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=a+4ba⋆b=a+4b Find each of the following: 7⋆6=7⋆6= 5⋆5=5⋆5= 6⋆7=6⋆7= z⋆s=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=Let A = N × N and ∗ be the binary operation on A defined by(a, b) ∗ (c, d) = (a + c, b + d) Show that ∗ is commutative and associative. Find the identity element for ∗ on A, if any.Define the binary operator ⋆⋆ by: a⋆b=a+8ba⋆b=a+8b Find each of the following: 3⋆4=3⋆4= 9⋆9=9⋆9= 4⋆3=4⋆3= z⋆c=z⋆c=
- Define the binary operator # by: aa#b=b= the larger value of aa or bb.; Find each of the following: 99#3=3= 88#8=8= 33#9=9=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: a∇b=5a∇b=5 Simplify each of the following. Do the order of operations (do what is in parentheses first). (5∇4)∇2(5∇4)∇2 = (6∇3)∇7(6∇3)∇7