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Symbol Notation - Intermediate-Advanced Level: logical symbols INTERMEDIATE-ADVANCED

Ready to master symbol notation? This time-bound test features 20 intermediate-advanced-level challenges. Worksheet 22 of 30 sharpens your logical symbols skills. Master symbolic logic, notation puzzles, symbol interpretation through guided practice. Perfect for advanced developing test preparation.

📝 Worksheet 22 of 30 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Intermediate-advanced level

What you'll learn in this worksheet:
Your progress through Symbol Notation
Worksheet 22 of 30 (73% complete)

Question 1

If ♢ = +, □ = ÷ (standard order of operations applies), then evaluate: 4 ♢ 8 □ 2
Substituting symbols: 4 + 8 ÷ 2
Applying order of operations: = 8
arithmetic, basic

Question 2

If '≼' means '≤', then determine: 7 ≼ 4
≼ = ≤
7 ≤ 4 is False
inequality, comparison

Question 3

If g(x) = x² + 1, then find g(9)
Substituting x = 9:
9² + 1 = 82
functions, substitution

Question 4

Given: A = {3, 4, 6, 9} B = {2, 4, 5, 8, 10} C = {2, 4, 5, 7, 8} Find: C − B
Difference of C and B:
{2, 4, 5, 7, 8} − {2, 4, 5, 8, 10} = {7}
sets, operations

Question 5

If ⊖ = -, ☆ = - (standard order of operations applies), then evaluate: 10 ⊖ 6 ☆ 1
Substituting symbols: 10 - 6 - 1
Applying order of operations: = 3
arithmetic, basic

Question 6

Given: A = {1, 2, 4, 6, 10} B = {1, 4, 7, 9} C = {1, 3, 5, 7} Find: A ∩ B
Intersection of A and B:
{1, 2, 4, 6, 10} ∩ {1, 4, 7, 9} = {1, 4}
sets, operations

Question 7

If ⊗ = ×, ◇ = ÷ (standard order of operations applies), then evaluate: 3 ⊗ 2 ◇ 9
Substituting symbols: 3 × 2 ÷ 9
Applying order of operations: = 0
arithmetic, basic

Question 8

If '≠' means '≠', then determine: 1 ≠ 9
≠ = ≠
1 ≠ 9 is True
inequality, comparison

Question 9

If ♡ = ÷, ∇ = - (standard order of operations applies), then evaluate: 7 ♡ 9 ∇ 4
Substituting symbols: 7 ÷ 9 - 4
Applying order of operations: = -4
arithmetic, basic

Question 10

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: r(f(5))
Evaluate from innermost outward:
r(f(5))
= 36
nested, functions, advanced

Question 11

Given matrices: A = [ 3 1] [ 3 1] B = [ 3 5] [ 4 2] Compute: A - B
Matrix subtraction:
A - B =

[ 0 -4]
[-1 -1]
matrix, advanced

Question 12

In the notation system where ☀ means x³, what is the value of ☀(6)?
Applying ☀ to 6:
6³ = 216
complex, systems

Question 13

If ♡ = ÷, ♧ = × (standard order of operations applies), then evaluate: 15 ♡ 4 ♧ 12
Substituting symbols: 15 ÷ 4 × 12
Applying order of operations: = 0
arithmetic, basic

Question 14

If P = True, Q = True, and 'xor' means XOR, then evaluate: P xor Q
Logical operation: XOR
P=True, Q=True → XOR is True when inputs differ
Result: False
logic, boolean

Question 15

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: r(g(p(6)))
Evaluate from innermost outward:
r(g(p(6)))
= 322
nested, functions, advanced

Question 16

If f(x) = √x, then find f(1)
Substituting x = 1:
√1 = 4
functions, substitution

Question 17

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

Question 18

If ◇ = ÷, ♡ = ÷ (standard order of operations applies), then evaluate: 5 ◇ 9 ♡ 6
Substituting symbols: 5 ÷ 9 ÷ 6
Applying order of operations: = 5
arithmetic, basic

Question 19

Given matrices: A = [ 3 3] [ 1 2] B = [ 3 4] [ 2 3] Compute: A × B
Matrix multiplication:
A × B =

[15 21]
[ 7 10]
matrix, advanced

Question 20

In the notation system where ☆ means x², what is the value of ☆(4)?
Applying ☆ to 4:
4² = 16
complex, systems
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