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Symbol Notation - Advanced Level: inequality symbols ADVANCED

Master symbol notation concepts through this hard problem set practice set. Worksheet 26 of 30 contains 20 advanced-level problems. Deep dive into inequality symbols while learning notation systems, symbol relationships, logical symbols. Recommended for advanced learners aiming for complex scenarios and multi-step problems.

📝 Worksheet 26 of 30 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Advanced level

What you'll learn in this worksheet:
Your progress through Symbol Notation
Worksheet 26 of 30 (86% complete)

Question 1

In the notation system where ◀ means x + 5, what is the value of ◀(6)?
Applying ◀ to 6:
6 + 5 = 11
complex, systems

Question 2

If ⊖ = -, ⊕ = + (standard order of operations applies), then evaluate: 14 ⊖ 3 ⊕ 1
Substituting symbols: 14 - 3 + 1
Applying order of operations: = 12
arithmetic, basic

Question 3

In the notation system where ☽ means x - 5, what is the value of ☽(3)?
Applying ☽ to 3:
3 - 5 = -2
complex, systems

Question 4

If ★ = +, ♡ = ÷ (standard order of operations applies), then evaluate: 6 ★ 7 ♡ 9
Substituting symbols: 6 + 7 ÷ 9
Applying order of operations: = 6
arithmetic, basic

Question 5

Given: A = {1, 2, 6, 7, 10} B = {3, 5, 6, 8, 10} C = {1, 2, 3, 7, 8, 9} Find: B ∩ C
Intersection of B and C:
{3, 5, 6, 8, 10} ∩ {1, 2, 3, 7, 8, 9} = {3, 8}
sets, operations

Question 6

In the notation system where ▼ means x² - 1, what is the value of ▼(6)?
Applying ▼ to 6:
6² - 1 = 35
complex, systems

Question 7

If f(x)=x+2, g(x)=2x, h(x)=x², p(x)=x-3, q(x)=x/2, r(x)=3x-1, then evaluate: p(q(h(2)))
Evaluate from innermost outward:
p(q(h(2)))
= -1
nested, functions, advanced

Question 8

If g(x) = 2x - 3, then find g(7)
Substituting x = 7:
27 - 3 = 24
functions, substitution

Question 9

If f(x)=x+2, g(x)=2x, h(x)=x², p(x)=x-3, q(x)=x/2, r(x)=3x-1, then evaluate: p(g(h(6)))
Evaluate from innermost outward:
p(g(h(6)))
= 233
nested, functions, advanced

Question 10

In the notation system where ◆ means 2x + 1, what is the value of ◆(7)?
Applying ◆ to 7:
27 + 1 = 28
complex, systems

Question 11

If k(x) = x - 8, then find k(8)
Substituting x = 8:
8 - 8 = 0
functions, substitution

Question 12

If P = True, Q = False, and 'nor' means NOR, then evaluate: P nor Q
Logical operation: NOR
P=True, Q=False → NOR is True only when both are False
Result: False
logic, boolean

Question 13

Given: A = {2, 3, 7, 10} B = {3, 5, 6, 7, 10} C = {1, 7, 9, 10} Find: A ∩ B
Intersection of A and B:
{2, 3, 7, 10} ∩ {3, 5, 6, 7, 10} = {3, 7, 10}
sets, operations

Question 14

If f(x)=x+2, g(x)=2x, h(x)=x², p(x)=x-3, q(x)=x/2, r(x)=3x-1, then evaluate: h(g(r(2)))
Evaluate from innermost outward:
h(g(r(2)))
= 53361
nested, functions, advanced

Question 15

If '≽' means '≥', then determine: 19 ≽ 4
≽ = ≥
19 ≥ 4 is True
inequality, comparison

Question 16

In the notation system where ◆ means 2x + 1, what is the value of ◆(3)?
Applying ◆ to 3:
23 + 1 = 24
complex, systems

Question 17

If '≽' means '≥', then determine: 2 ≽ 14
≽ = ≥
2 ≥ 14 is False
inequality, comparison

Question 18

If f(x)=x+2, g(x)=2x, h(x)=x², p(x)=x-3, q(x)=x/2, r(x)=3x-1, then evaluate: g(r(3))
Evaluate from innermost outward:
g(r(3))
= 232
nested, functions, advanced

Question 19

In the notation system where ▶ means x - 2, what is the value of ▶(8)?
Applying ▶ to 8:
8 - 2 = 6
complex, systems

Question 20

If □ = ÷, ∇ = - (standard order of operations applies), then evaluate: 5 □ 14 ∇ 7
Substituting symbols: 5 ÷ 14 - 7
Applying order of operations: = -7
arithmetic, basic
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