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13 Apr 2022: construct the tangents from A and A′ to the circles and determine their intersections B, B′, C and C′. ... b)B. C. A = A′. B′. C′. (c). Fig. 6. Movement process of a crinkle linkage.

2 Nov 2022: Thenbreadth-first search to depth d examines (bd1 1)/(b 1) nodes, which is O(bd ),ignoring the constant factor of b/(b 1). ... 1). Korf [7] shows that the time needed for iterative deepening to reach depth d isonly b/(b 1) times that for breadth-first

23 May 2022: i) Prove that, for all a, b N+, if a > b then gcd(a, b) = gcd(a b, b).[4 marks]. ... Briefly justify youranswer. [2 marks]. (b) Prove that there is no surjection from N to(N {0, 1}.

9 May 2022: B[[B]](s) = >. 〈if B then C1 else C2,〈s,h〉〉 〈C1,〈s,h〉〉. B[[B]](s) =. 〈if B then C1 else C2,〈s,h〉〉 〈C2,〈s,h〉〉. B[[B]](s) =. ... B[[B]](s) = >. 〈while B do C,〈s,h〉〉 〈C ; while B do C,〈s,h〉〉.

3 Jun 2022: f g α Bij(A,A).β Bij(B,B). β f = g α. Prove that is an equivalence relation on (A B). ... 2 marks]. (B) What is the cardinality of Sn for each n N?

5 Sep 2022: i) dne : A A [3 marks]. (ii) contra : (A B) (B A) [4 marks]. ... unzip : {A : Set}{B : Set}{n : Nat}Vec (AB) n Vec A nVec B n.

5 Sep 2022: b) Let K3 denote the graph with three vertices a,b,c and the three edges{a,b},{b,c} and {a,c}. ... 5 marks]. (d) Let K2 denote the graph consisting of two vertices a and b and the single edge{a,b}.

26 Jan 2022: 5. The red star in a cataclysmic variable has a surface magnetic field B. ... B=. (. R. R. )3. at a distance R from the centre of the star which has radius R.

3 Jun 2022: a A]{0,1} [b B]{0,1} [c C]{1,n} [d D]{1,1}. where A is a finite set of characters from the alphabet, Σ; similarly for B, ... 1 mark]. (b) We can hypothesise that matches of the following pattern are always validconstructions in English:.

23 May 2022: B. A. (a) Shortest paths. (i) What is the definition of a shortest path? ... 1 mark]. (ii) How many shortest paths are there from node A to node B?