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Symbol Notation - Expert Level: directional symbols EXPERT

Comprehensive self assessment worksheet covering 20 expert-level symbol notation problems. Worksheet 28 of 30 emphasizes directional symbols. Master logical symbols, notation decoding, symbolic reasoning through detailed explanations. Difficulty: challenging problems and time-bound practice. Tailored for expert-level preparation.

📝 Worksheet 28 of 30 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Expert level

What you'll learn in this worksheet:
Your progress through Symbol Notation
Worksheet 28 of 30 (93% complete)

Question 1

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

[ 1 -2]
[ 1 0]
matrix, advanced

Question 2

If P = False, Q = False, and '<->' means IFF, then evaluate: P <-> Q
Logical operation: IFF
P=False, Q=False → IFF is True when both are same
Result: True
logic, boolean

Question 3

If ◆ = ×, □ = ÷ (standard order of operations applies), then evaluate: 5 ◆ 15 □ 10
Substituting symbols: 5 × 15 ÷ 10
Applying order of operations: = 5
arithmetic, basic

Question 4

If P = False, Q = False, and '->' means IMPLIES, then evaluate: P -> Q
Logical operation: IMPLIES
P=False, Q=False → IMPLIES is False only when P=True and Q=False
Result: True
logic, boolean

Question 5

If '≽' means '≥', then determine: 5 ≽ 7
≽ = ≥
5 ≥ 7 is False
inequality, comparison

Question 6

If P = True, Q = False, and '&' means AND, then evaluate: P & Q
Logical operation: AND
P=True, Q=False → AND gives True only if both True
Result: False
logic, boolean

Question 7

Given matrices: A = [ 5 5] [ 3 3] B = [ 5 5] [ 3 4] Compute: A × B
Matrix multiplication:
A × B =

[40 45]
[24 27]
matrix, advanced

Question 8

Given: A = {4, 6, 7, 9, 10} B = {4, 7, 9} C = {1, 3, 5, 6, 7, 10} Find: B △ C
Symmetric Difference of B and C:
{4, 7, 9} △ {1, 3, 5, 6, 7, 10} = {1, 3, 4, 5, 6, 9, 10}
sets, operations

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

Question 10

In the notation system where ▶ means x - 2, what is the value of ▶(4)?
Applying ▶ to 4:
4 - 2 = 2
complex, systems

Question 11

Given: A = {3, 4, 5, 7, 9} B = {1, 2, 6, 7, 10} C = {1, 3, 4, 6, 8, 9} Find: C ∩ A
Intersection of C and A:
{1, 3, 4, 6, 8, 9} ∩ {3, 4, 5, 7, 9} = {3, 4, 9}
sets, operations

Question 12

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: f(p(r(6)))
Evaluate from innermost outward:
f(p(r(6)))
= 34
nested, functions, advanced

Question 13

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

Question 14

If ⊕ = +, ⊘ = ÷ (standard order of operations applies), then evaluate: 12 ⊕ 15 ⊘ 15
Substituting symbols: 12 + 15 ÷ 15
Applying order of operations: = 13
arithmetic, basic

Question 15

If k(x) = x² - 1, then find k(10)
Substituting x = 10:
10² - 1 = 99
functions, substitution

Question 16

In the notation system where ☆ means x², what is the value of ☆(3)?
Applying ☆ to 3:
3² = 9
complex, systems

Question 17

Given: A = {3, 4, 5, 9} B = {1, 3, 4, 6, 8, 9} C = {2, 3, 6, 7, 8} Find: A − B
Difference of A and B:
{3, 4, 5, 9} − {1, 3, 4, 6, 8, 9} = {5}
sets, operations

Question 18

If k(x) = x/4, then find k(9)
Substituting x = 9:
9/4 = 2.25
functions, substitution

Question 19

Given: A = {1, 6, 7} B = {1, 2, 4, 7, 9} C = {1, 4, 7, 8, 9, 10} Find: C ∪ A
Union of C and A:
{1, 4, 7, 8, 9, 10} ∪ {1, 6, 7} = {1, 4, 6, 7, 8, 9, 10}
sets, operations

Question 20

If P = True, Q = False, and '->' means IMPLIES, then evaluate: P -> Q
Logical operation: IMPLIES
P=True, Q=False → IMPLIES is False only when P=True and Q=False
Result: False
logic, boolean
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